Research outputs
2024
New examples of twisted Brill–Noether loci I
Brambila-Paz, L., & Newstead, P. E. (2024). New examples of twisted Brill–Noether loci I. International Journal of Mathematics, 35(09). doi:10.1142/s0129167x24410039
2023
Stability and deformations of generalised Picard sheaves
Biswas, I., Brambila-Paz, L., & Newstead, P. E. (2023). Stability and deformations of generalised Picard sheaves. MANUSCRIPTA MATHEMATICA. doi:10.1007/s00229-023-01468-5
2022
New examples of twisted Brill-Noether loci I
Higher rank Brill—Noether theory and coherent systems open questions
Newstead, P. (2022). Higher rank Brill—Noether theory and coherent systems open questions. Proyecciones (Antofagasta), 41(2), 449-480. doi:10.22199/issn.0717-6279-5276
2021
Coherent Systems on the Projective Line
Newstead, P., & Teixidor i Bigas, M. (2021). Coherent Systems on the Projective Line. The Quarterly Journal of Mathematics, 72(1-2), 115-136. doi:10.1093/qmathj/haaa024
2020
Nonemptiness and smoothness of twisted Brill-Noether loci
Hitching, G. H., Hoff, M., & Newstead, P. E. (2020). Nonemptiness and smoothness of twisted Brill-Noether loci. Annali di Matematica Pura ed Applicata. doi:10.1007/s10231-020-01009-x
Coherent systems on the projective line
Seshadri constants and Grassmann bundles over curves
Biswas, I., Hanumanthu, K., Nagaraj, D. S., & Newstead, P. E. (2021). Seshadri constants and Grassmann bundles over curves. Annales de l'Institut Fourier, 70(4), 1477-1496. doi:10.5802/aif.3370
2019
Generated coherent systems and a conjecture of D. C. Butler
Brambila-Paz, L., Mata-Gutiérrez, O., Newstead, P. E., & Ortega, A. (2019). Generated coherent systems and a conjecture of D. C. Butler. International Journal of Mathematics, 30(05), 1950024. doi:10.1142/s0129167x19500241
HIGGS BUNDLES OVER ELLIPTIC CURVES FOR COMPLEX REDUCTIVE GROUPS
FRANCO, E., GARCIA-PRADA, O., & NEWSTEAD, P. E. (2019). HIGGS BUNDLES OVER ELLIPTIC CURVES FOR COMPLEX REDUCTIVE GROUPS. Glasgow Mathematical Journal, 61(2), 297-320. doi:10.1017/s0017089518000228
Higgs bundles over elliptic curves for real groups
Franco, E., García-Prada, O., & Newstead, P. E. (2019). Higgs bundles over elliptic curves for real groups. The Quarterly Journal of Mathematics, 70(1), 105-146. doi:10.1093/qmath/hay037
2018
Stability and deformations of generalised Picard sheaves
Higher rank BN-theory for curves of genus 6
Lange, H., & Newstead, P. E. (2018). Higher rank BN-theory for curves of genus 6. International Journal of Mathematics, 29(02), 1850014. doi:10.1142/s0129167x18500143
Some examples of rank-2 Brill–Noether loci
Newstead, P. E. (2018). Some examples of rank-2 Brill–Noether loci. Revista Matemática Complutense, 31(1), 201-215. doi:10.1007/s13163-017-0241-6
2017
Higher rank BN-theory for curves of genus 4
Lange, H., & Newstead, P. E. (2017). Higher rank BN-theory for curves of genus 4. Communications in Algebra, 45(9), 3948-3966. doi:10.1080/00927872.2016.1251938
2016
Higher rank BN-theory for curves of genus 5
Lange, H., & Newstead, P. E. (2016). Higher rank BN-theory for curves of genus 5. Revista Matemática Complutense, 29(3), 691-717. doi:10.1007/s13163-016-0203-4
VBAC: A Brief History
Newstead, P. (2016). VBAC: A Brief History. In International Journal of Mathematics Vol. 27 (pp. 1602002). World Scientific Pub Co Pte Lt. doi:10.1142/s0129167x1602002x
Nonemptiness of Brill–Noether Loci in<i>M</i>(2,<i>K</i>)
Lange, H., Newstead, P. E., & Park, S. S. (2016). Nonemptiness of Brill–Noether Loci in<i>M</i>(2,<i>K</i>). Communications in Algebra, 44(2), 746-767. doi:10.1080/00927872.2014.990020
2015
Nonemptiness of Brill–Noether loci in M(2,L)
Lange, H., Newstead, P. E., & Strehl, V. (2015). Nonemptiness of Brill–Noether loci in M(2,L). International Journal of Mathematics, 26(13), 1550108. doi:10.1142/s0129167x15501086
On linear series and a conjecture of D. C. Butler
Bhosle, U. N., Brambila-Paz, L., & Newstead, P. E. (2015). On linear series and a conjecture of D. C. Butler. International Journal of Mathematics, 26(02), 1550007. doi:10.1142/s0129167x1550007x
2014
Higgs bundles over elliptic curves
Franco, E., Garcia-Prada, O., & Newstead, P. E. (2014). Higgs bundles over elliptic curves. Illinois Journal of Mathematics, 58(1). doi:10.1215/ijm/1427897168
On coherent systems with fixed determinant
Grzegorczyk, I., & Newstead, P. E. (2014). On coherent systems with fixed determinant. International Journal of Mathematics, 25(05), 1450045. doi:10.1142/s0129167x14500451
2013
Bundles of rank 3 on curves of Clifford index 3
Lange, H., & Newstead, P. E. (2013). Bundles of rank 3 on curves of Clifford index 3. Journal of Symbolic Computation, 57, 3-18. doi:10.1016/j.jsc.2013.05.002
Bundles computing Clifford indices on trigonal curves
Lange, H., & Newstead, P. E. (2013). Bundles computing Clifford indices on trigonal curves. Archiv der Mathematik, 101(1), 21-31. doi:10.1007/s00013-013-0540-1
Hodge polynomials of SL $$(2,\mathbb{C })$$ -character varieties for curves of small genus
Logares, M., Muñoz, V., & Newstead, P. E. (2013). Hodge polynomials of SL $$(2,\mathbb{C })$$ -character varieties for curves of small genus. Revista Matemática Complutense, 26(2), 635-703. doi:10.1007/s13163-013-0115-5
Vector Bundles of Rank 2 Computing Clifford Indices
Lange, H., & Newstead, P. E. (2013). Vector Bundles of Rank 2 Computing Clifford Indices. Communications in Algebra, 41(6), 2317-2345. doi:10.1080/00927872.2012.658532
On bundles of rank 3 computing Clifford indices
Lange, H., & Newstead, P. E. (2013). On bundles of rank 3 computing Clifford indices. Kyoto Journal of Mathematics, 53(1). doi:10.1215/21562261-1966062
2012
Bundles of rank 2 with small Clifford index
Newstead, P. E. (2012). Bundles of rank 2 with small Clifford index. In C. Faber, G. Farkas, & R. de Jong (Eds.), Geometry and Arithmetic (pp. 267-281). Zurich: European Mathematical Society.
Introduction to Moduli Problems and Orbit Spaces
Newstead, P. E. (2012). Introduction to Moduli Problems and Orbit Spaces (Vol. 51). Mumbai: Narosa Publishing House.
ON AN EXAMPLE OF MUKAI
LANGE, H., MERCAT, V., & NEWSTEAD, P. E. (2012). ON AN EXAMPLE OF MUKAI. Glasgow Mathematical Journal, 54(2), 261-271. doi:10.1017/s0017089511000577
2011
STABLE BUNDLES OF RANK 2 WITH FOUR SECTIONS
GRZEGORCZYK, I., MERCAT, V., & NEWSTEAD, P. E. (2011). STABLE BUNDLES OF RANK 2 WITH FOUR SECTIONS. International Journal of Mathematics, 22(12), 1743-1762. doi:10.1142/s0129167x11007434
<i>Koszul cohomology and algebraic geometry</i> (University Lecture Series 52)
Newstead, P. (2011). <i>Koszul cohomology and algebraic geometry</i> (University Lecture Series 52). Bulletin of the London Mathematical Society, 43(2), 411-414. doi:10.1112/blms/bdq134
Existence of alpha-stable coherent systems on algebraic curves
Newstead, P. E. (2011). Existence of alpha-stable coherent systems on algebraic curves. In Grassmannians, Moduli Spaces and Vector Bundles (pp. 121-140). Providence RI: American Mathematical Society.
Lower bounds for Clifford indices in rank three
LANGE, H., & NEWSTEAD, P. E. (2011). Lower bounds for Clifford indices in rank three. Mathematical Proceedings of the Cambridge Philosophical Society, 150(1), 23-33. doi:10.1017/s0305004110000502
2010
Further examples of stable bundles of rank 2 with 4 sections
Lange, H., & Newstead, P. E. (2010). Further examples of stable bundles of rank 2 with 4 sections. Retrieved from https://arxiv.org/abs/1011.0849v1
Generation of vector bundles computing Clifford indices
Lange, H., & Newstead, P. E. (2010). Generation of vector bundles computing Clifford indices. Archiv der Mathematik, 94(6), 529-537. doi:10.1007/s00013-010-0126-0
Vector Bundles and Complex Geometry
Garcia-Prada, O., Newstead, P. E., & others. (Eds.) (2010). Vector Bundles and Complex Geometry (Vol. 522). Providence RI: American Mathematical Society.
2009
Lower bounds for Clifford indices in rank three
Lange, H., & Newstead, P. E. (2009). Lower bounds for Clifford indices in rank three. Retrieved from https://arxiv.org/abs/0912.2618v1
Generation of vector bundles computing Clifford indices
Lange, H., & Newstead, P. E. (2009). Generation of vector bundles computing Clifford indices. Retrieved from https://arxiv.org/abs/0912.0815v2
Hodge polynomials and birational types of moduli spaces of coherent systems on elliptic curves
Lange, H., & Newstead, P. E. (2009). Hodge polynomials and birational types of moduli spaces of coherent systems on elliptic curves. manuscripta mathematica, 130(1), 1-19. doi:10.1007/s00229-009-0276-1
Moduli Spaces of Coherent Systems of Small Slope on Algebraic Curves
Bradlow, S. B., García-Prada, O., Mercat, V., Muñoz, V., & Newstead, P. E. (2009). Moduli Spaces of Coherent Systems of Small Slope on Algebraic Curves. Communications in Algebra, 37(8), 2649-2678. doi:10.1080/00927870902747464
Geometric Invariant Theory
Newstead, P. E. (2009). Geometric Invariant Theory. In S. B. Bradlow, L. Brambila-Paz, & O. Garcia-Prada (Eds.), Moduli Spaces and Vectr Bundles (pp. 99-127). Cambridge: Cambridge University Press.
Moduli spaces of coherent systems of small slope
Bradlow, S. B., Garcia-Prada, O., Mercat, V., Munoz, V., & Newstead, P. E. (2009). Moduli spaces of coherent systems of small slope. Comm. in Algebra, 37(8), 2649-2978.
Stability of projective Poincaré and Picard bundles
Biswas, I., Brambila-Paz, L., & Newstead, P. E. (2009). Stability of projective Poincaré and Picard bundles. Bulletin of the London Mathematical Society, 41(3), 458-472. doi:10.1112/blms/bdp017
2008
Clifford indices for vector bundles on curves
Lange, H., & Newstead, P. E. (2008). Clifford indices for vector bundles on curves. Retrieved from https://arxiv.org/abs/0811.4680v3
COHERENT SYSTEMS OF GENUS 0 III: COMPUTATION OF FLIPS FOR k = 1
LANGE, H., & NEWSTEAD, P. E. (2008). COHERENT SYSTEMS OF GENUS 0 III: COMPUTATION OF FLIPS FOR k = 1. International Journal of Mathematics, 19(09), 1103-1119. doi:10.1142/s0129167x08005047
On coherent systems of type (n, d, n + 1) on Petri curves
Bhosle, U. N., Brambila-Paz, L., & Newstead, P. E. (2008). On coherent systems of type (n, d, n + 1) on Petri curves. manuscripta mathematica, 126(4), 409-441. doi:10.1007/s00229-008-0190-y
Clifford’s theorem for coherent systems
Lange, H., & Newstead, P. E. (2008). Clifford’s theorem for coherent systems. Archiv der Mathematik, 90(3), 209-216. doi:10.1007/s00013-007-2534-3
2007
Coherent systems of genus 0, III: Computation of flips for k=1
Lange, H., & Newstead, P. E. (2007). Coherent systems of genus 0, III: Computation of flips for k=1. Retrieved from https://arxiv.org/abs/0707.1466v2
Moduli spaces of coherent systems of small slope on algebraic curves
COHERENT SYSTEMS OF GENUS 0 II: EXISTENCE RESULTS FOR k ≥ 3
LANGE, H., & NEWSTEAD, P. E. (2007). COHERENT SYSTEMS OF GENUS 0 II: EXISTENCE RESULTS FOR k ≥ 3. International Journal of Mathematics, 18(04), 363-393. doi:10.1142/s0129167x07004072
ON THE GEOMETRY OF MODULI SPACES OF COHERENT SYSTEMS ON ALGEBRAIC CURVES
BRADLOW, S. B., GARCÍA-PRADA, O., MERCAT, V., MUÑOZ, V., & NEWSTEAD, P. E. (2007). ON THE GEOMETRY OF MODULI SPACES OF COHERENT SYSTEMS ON ALGEBRAIC CURVES. International Journal of Mathematics, 18(04), 411-453. doi:10.1142/s0129167x07004151
2006
Universal families on moduli spaces of principal bundles on curves
Balaji, V., Biswas, I., Nagaraj, D. S., & Newstead, P. E. (2006). Universal families on moduli spaces of principal bundles on curves. International Mathematics Research Notices. doi:10.1155/imrn/2006/80641
Deformations of the generalised Picard bundle
Biswas, I., Brambila-Paz, L., & Newstead, P. E. (2006). Deformations of the generalised Picard bundle. Topology, 45(2), 403-419. doi:10.1016/j.top.2005.08.004
Universal Families on moduli spaces of principal bundles on curves
Balaji, V., Biswas, I., Nagaraj, D. S., & Newstead, P. E. (2006). Universal Families on moduli spaces of principal bundles on curves. Retrieved from https://arxiv.org/abs/math/0601168v1
On Clifford's theorem for rank-3 bundles
Lange, H., & Newstead, P. E. (2006). On Clifford's theorem for rank-3 bundles. REVISTA MATEMATICA IBEROAMERICANA, 22(1), 287-304. Retrieved from https://www.webofscience.com/
2005
COHERENT SYSTEMS ON ELLIPTIC CURVES
LANGE, H., & NEWSTEAD, P. E. (2005). COHERENT SYSTEMS ON ELLIPTIC CURVES. International Journal of Mathematics, 16(07), 787-805. doi:10.1142/s0129167x05003090
On Poincaré bundles of vector bundles on curves
Lange, H., & Newstead, P. E. (2005). On Poincaré bundles of vector bundles on curves. manuscripta mathematica, 117(2), 173-181. doi:10.1007/s00229-005-0553-6
'Algebraic Quotients. Torus Actions. The Adjoint Representation and the Adjoint Action'
Newstead, P. E. (2005). 'Algebraic Quotients. Torus Actions. The Adjoint Representation and the Adjoint Action'. Unknown Journal, 107(4), 25-27.
2004
COHERENT SYSTEMS OF GENUS 0
LANGE, H., & NEWSTEAD, P. E. (2004). COHERENT SYSTEMS OF GENUS 0. International Journal of Mathematics, 15(04), 409-424. doi:10.1142/s0129167x04002326
2003
On Clifford’s theorem for rank-3 bundles
Lange, H., & Newstead, P. E. (2006). On Clifford’s theorem for rank-3 bundles. Revista Matemática Iberoamericana, 22(1), 287-304. doi:10.4171/rmi/456
Coherent Systems and Brill–Noether Theory
Bradlow, S. B., García-Prada, O., Muñoz, V., & Newstead, P. E. (2003). Coherent Systems and Brill–Noether Theory. International Journal of Mathematics, 14(07), 683-733. doi:10.1142/s0129167x03002009
2002
Maximal Subbundles and Gromov-Witten Invariants
Lange, H., & Newstead, P. E. (2002). Maximal Subbundles and Gromov-Witten Invariants. Retrieved from https://arxiv.org/abs/math/0204216v2
Stability of the Picard Bundle
Biswas, I., Brambila‐Paz, L., Gómez, T. L., & Newstead, P. E. (2002). Stability of the Picard Bundle. Bulletin of the London Mathematical Society, 34(5), 561-568. doi:10.1112/s0024609302001170
2001
ON CLIFFORD'S THEOREM FOR VECTOR BUNDLES ON ALGEBRAIC CURVES
Ballico, E., & Newstead, P. E. (2001). ON CLIFFORD'S THEOREM FOR VECTOR BUNDLES ON ALGEBRAIC CURVES. Communications in Algebra, 29(8), 3223-3237. doi:10.1081/agb-100105018
2000
NONEMPTINESS OF BRILL–NOETHER LOCI
BRAMBILA-PAZ, L., MERCAT, V., NEWSTEAD, P. E., & ONGAY, F. (2000). NONEMPTINESS OF BRILL–NOETHER LOCI. International Journal of Mathematics, 11(06), 737-760. doi:10.1142/s0129167x00000350
1998
On the cohomology ring of the moduli space of rank 2 vector bundles on a curve
King, A. D., & Newstead, P. E. (1998). On the cohomology ring of the moduli space of rank 2 vector bundles on a curve. Topology, 37(2), 407-418. doi:10.1016/s0040-9383(97)00041-4
1997
Geography of Brill-Noether loci for small slopes
Brambila-Paz, L., Grzegorczyk, I., & Newstead, P. E. (1997). Geography of Brill-Noether loci for small slopes. Journal of Algebraic Geometry, 6(4), 645-669.
Algebraic cohomology of the moduli space of rank 2 vector bundles on a curve
Balaji, V., King, A. D., & Newstead, P. E. (1997). Algebraic cohomology of the moduli space of rank 2 vector bundles on a curve. Topology, 36(2), 567-577. doi:10.1016/0040-9383(96)00007-9
Stability of the Poincaré Bundle
Balaji, V., Brambila‐Paz, L., & Newstead, P. E. (1997). Stability of the Poincaré Bundle. Mathematische Nachrichten, 188(1), 5-15. doi:10.1002/mana.19971880102
1995
Geography of Brill-Noether loci for small slopes
Paz, L. B., Grzegorczyk, I., & Newstead, P. E. (1995). Geography of Brill-Noether loci for small slopes. doi:10.48550/arxiv.alg-geom/9511003
1986
On the geometry of the planar 4-bar mechanism
Gibson, C. G., & Newstead, P. E. (1986). On the geometry of the planar 4-bar mechanism. Acta Applicandae Mathematicae, 7(2), 113-135. doi:10.1007/bf00051348
1985
Uniform Bundles on Quadric Surfaces and Some Related Varieties
Ballico, E., & Newstead, P. E. (1985). Uniform Bundles on Quadric Surfaces and Some Related Varieties. Journal of the London Mathematical Society, s2-31(2), 211-223. doi:10.1112/jlms/s2-31.2.211
1984
On the relations between characteristic classes of stable bundles of rank 2 over an algebraic curve
Newstead, P. E. (1984). On the relations between characteristic classes of stable bundles of rank 2 over an algebraic curve. Bulletin of the American Mathematical Society, 10(2), 292-294. doi:10.1090/s0273-0979-1984-15252-2
1983
A Space Curve whose Normal Bundle is Stable
Newstead, P. E. (1983). A Space Curve whose Normal Bundle is Stable. Journal of the London Mathematical Society, s2-28(3), 428-434. doi:10.1112/jlms/s2-28.3.428
On the Plane Sections of a Quadric Hypersurface
Newstead, P. E. (1983). On the Plane Sections of a Quadric Hypersurface. Bulletin of the London Mathematical Society, 15(3), 226-228. doi:10.1112/blms/15.3.226
Pencils on Conic Bundles
Newstead, P. E. (1983). Pencils on Conic Bundles. Journal of the London Mathematical Society, s2-27(1), 19-28. doi:10.1112/jlms/s2-27.1.19
1982
ON THE COHOMOLOGY AND THE PICARD GROUP OF A MODULI SPACE OF BUNDLES ON P<sup>3</sup>
NEWSTEAD, P. E. (1982). ON THE COHOMOLOGY AND THE PICARD GROUP OF A MODULI SPACE OF BUNDLES ON P<sup>3</sup>. The Quarterly Journal of Mathematics, 33(3), 349-355. doi:10.1093/qmath/33.3.349
Covariants of pencils of binary cubics
Newstead, P. E. (1982). Covariants of pencils of binary cubics. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 91(3-4), 181-183. doi:10.1017/s0308210500017431
Quadratic complexes. II
Newstead, P. E. (1982). Quadratic complexes. II. Mathematical Proceedings of the Cambridge Philosophical Society, 91(2), 183-206. doi:10.1017/s0305004100059247
1981
Comparison theorems for conic bundles
Newstead, P. E. (1981). Comparison theorems for conic bundles. Mathematical Proceedings of the Cambridge Philosophical Society, 90(1), 21-31. doi:10.1017/s0305004100058497
Invariants of pencils of binary cubics
Newstead, P. E. (1981). Invariants of pencils of binary cubics. Mathematical Proceedings of the Cambridge Philosophical Society, 89(2), 201-209. doi:10.1017/s0305004100058102
Real classification of complex conics
Newstead, P. E. (1981). Real classification of complex conics. Mathematika, 28(1), 36-53. doi:10.1112/s0025579300015333
1980
Rationality of moduli spaces of stable bundles
Newstead, P. E. (1980). Rationality of moduli spaces of stable bundles. Mathematische Annalen, 249(3), 281-282. doi:10.1007/bf01363901
The fundamental group of a moduli space of bundles on P3
Newstead, P. E. (1980). The fundamental group of a moduli space of bundles on P3. Topology, 19(4), 419-426. doi:10.1016/0040-9383(80)90024-5
1975
Rationality of moduli spaces of stable bundles
Newstead, P. E. (1975). Rationality of moduli spaces of stable bundles. Mathematische Annalen, 215(3), 251-268. doi:10.1007/bf01343893
1973
A Non-Existence Theorem for Families of Stable Bundles
Newstead, P. E. (1973). A Non-Existence Theorem for Families of Stable Bundles. Journal of the London Mathematical Society, s2-6(2), 259-266. doi:10.1112/jlms/s2-6.2.259
1972
Characteristic classes of stable bundles of rank 2 over an algebraic curve
Newstead, P. E. (1972). Characteristic classes of stable bundles of rank 2 over an algebraic curve. Transactions of the American Mathematical Society, 169(0), 337-345. doi:10.1090/s0002-9947-1972-0316452-9
1968
Stable bundles of rank 2 and odd degree over a curve of genus 2
Newstead, P. E. (1968). Stable bundles of rank 2 and odd degree over a curve of genus 2. Topology, 7(3), 205-215. doi:10.1016/0040-9383(68)90001-3
1967
Topological properties of some spaces of stable bundles
Newstead, P. E. (1967). Topological properties of some spaces of stable bundles. Topology, 6(2), 241-262. doi:10.1016/0040-9383(67)90037-7
1964
Reducible vector bundles on a quadric surface
Newstead, P. E., & Schwarzenberger, R. L. E. (1964). Reducible vector bundles on a quadric surface. Mathematical Proceedings of the Cambridge Philosophical Society, 60(3), 421-424. doi:10.1017/s0305004100037920