Photo of Professor Aleksandr Pukhlikov

Professor Aleksandr Pukhlikov PhD in Mathematics, D.Sci.(Habil.) in Mathematics

Professor Mathematical Sciences

    Publications

    2020

    Birational geometry of singular Fano hypersurfaces of index two (Journal article)

    Pukhlikov, A. V. (2020). Birational geometry of singular Fano hypersurfaces of index two. Manuscripta Mathematica, 161(1-2), 161-203. doi:10.1007/s00229-018-1075-3

    DOI: 10.1007/s00229-018-1075-3

    Rationally connected rational double covers of primitive Fano varieties (Journal article)

    Pukhlikov, A. V. (n.d.). Rationally connected rational double covers of primitive Fano varieties. Épijournal de Géométrie Algébrique, 4. doi:10.46298/epiga.2020.volume4.5890

    DOI: 10.46298/epiga.2020.volume4.5890

    2019

    Canonical and log canonical thresholds of multiple projective spaces (Journal article)

    Pukhlikov, A. V. (2019). Canonical and log canonical thresholds of multiple projective spaces. European Journal of Mathematics. doi:10.1007/s40879-019-00388-7

    DOI: 10.1007/s40879-019-00388-7

    Birationally rigid finite covers of the projective space (Journal article)

    Pukhlikov, A. V. (2019). Birationally Rigid Finite Covers of the Projective Space. PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 307(1), 232-244. doi:10.1134/S0081543819060142

    DOI: 10.1134/S0081543819060142

    Birationally rigid complete intersections with a singular point of high multiplicity (Journal article)

    Pukhlikov, A. V. (2019). BIRATIONALLY RIGID COMPLETE INTERSECTIONS WITH A SINGULAR POINT OF HIGH MULTIPLICITY. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 62(1), 221-239. doi:10.1017/S0013091518000184

    DOI: 10.1017/S0013091518000184

    Birationally rigid complete intersections of high codimension (Journal article)

    Evans, D., & Pukhlikov, A. V. (2019). Birationally rigid complete intersections of high codimension. IZVESTIYA MATHEMATICS, 83(4), 743-769. doi:10.1070/IM8782

    DOI: 10.1070/IM8782

    Effective Birational Rigidity of Fano Double Hypersurfaces (Journal article)

    Eckl, T., & Pukhlikov, A. (2018). Effective Birational Rigidity of Fano Double Hypersurfaces. Arnold Mathematical Journal, 4(3-4), 505-521. doi:10.1007/s40598-019-00106-x

    DOI: 10.1007/s40598-019-00106-x

    2018

    Canonical and log canonical thresholds of Fano complete intersections (Journal article)

    Pukhlikov, A. V. (n.d.). Canonical and log canonical thresholds of Fano complete intersections. Retrieved from http://arxiv.org/abs/1704.00021v1

    DOI: 10.1007/s40879-017-0152-6

    Automorphisms of certain affine complements in the projective space (Journal article)

    Pukhlikov, A. V. (2018). Automorphisms of certain affine complements in projective space. SBORNIK MATHEMATICS, 209(2), 276-289. doi:10.1070/SM8839

    DOI: 10.1070/SM8839

    2017

    Factorial hypersurfaces (Journal article)

    Pukhlikov, A. V. (2017). Factorial Hypersurfaces. PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 299(1), 205-218. doi:10.1134/S0081543817080144

    DOI: 10.1134/S0081543817080144

    Birational geometry of algebraic varieties, fibred into Fano double spaces (Journal article)

    Pukhlikov, A. V. (2017). Birational geometry of algebraic varieties fibred into Fano double spaces. IZVESTIYA MATHEMATICS, 81(3), 618-644. doi:10.1070/IM8493

    DOI: 10.1070/IM8493

    The $4n^2$-inequality for complete intersection singularities (Journal article)

    Pukhlikov, A. V. (n.d.). The $4n^2$-inequality for complete intersection singularities. doi:10.1007/s40598-016-0060-8

    DOI: 10.1007/s40598-016-0060-8

    BIRATIONALLY RIGID COMPLETE INTERSECTIONS OF CODIMENSION TWO (Journal article)

    Evans, D., & Pukhlikov, A. (2017). BIRATIONALLY RIGID COMPLETE INTERSECTIONS OF CODIMENSION TWO. BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 54(5), 1627-1654. doi:10.4134/BKMS.b160683

    DOI: 10.4134/BKMS.b160683

    2016

    Birational geometry of Fano hypersurfaces of index two (Journal article)

    Pukhlikov, A. V. (2016). Birational geometry of Fano hypersurfaces of index two. Mathematische Annalen, 366(1-2), 721-782. doi:10.1007/s00208-015-1345-2

    DOI: 10.1007/s00208-015-1345-2

    On the global log canonical threshold of Fano complete intersections (Journal article)

    Eckl, T., & Pukhlikov, A. (2016). On the global log canonical threshold of Fano complete intersections. European Journal of Mathematics, 2(1), 291-303. doi:10.1007/s40879-015-0060-6

    DOI: 10.1007/s40879-015-0060-6

    The Gabrielov–Khovanskii Problem for Polynomials (Journal article)

    Pukhlikov, A. V. (2016). The Gabrielov–Khovanskii Problem for Polynomials. Arnold Mathematical Journal, 2(1), 29-68. doi:10.1007/s40598-015-0031-5

    DOI: 10.1007/s40598-015-0031-5

    2015

    Birationally rigid Fano fibre spaces. II (Journal article)

    Pukhlikov, A. (2015). Birationally rigid Fano fibre spaces. II. Izvestiya: Mathematics, 79(4), 809-837. doi:10.1070/IM2015v079n04ABEH002762

    DOI: 10.1070/IM2015v079n04ABEH002762

    Two inequalities for a sequence of blow-ups (Journal article)

    Pukhlikov, A. V. (2015). Two inequalities for a sequence of blow-ups. MATHEMATICAL NOTES, 97(5-6), 970-973. doi:10.1134/S0001434615050351

    DOI: 10.1134/S0001434615050351

    Birational Geometry of Higher-Dimensional Fano Varieties (Journal article)

    Pukhlikov, A. V. (2015). Birational Geometry of Higher-Dimensional Fano Varieties. PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 288, S1-S150. doi:10.1134/S0081543815030013

    DOI: 10.1134/S0081543815030013

    2014

    Birationally rigid Fano complete intersections. II (Journal article)

    Pukhlikov, A. V. (2014). Birationally rigid Fano complete intersections. II. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 688, 209-218. doi:10.1515/crelle-2012-0059

    DOI: 10.1515/crelle-2012-0059

    On the locus of non-rigid hypersurfaces (Conference Paper)

    Eckl, T., & Pukhlikov, A. V. (2014). On the locus of non-rigid hypersurfaces. In Springer Proceedings in Mathematics and Statistics Vol. 79 (pp. 121-139). Levico Terme, Italy: Springer. doi:10.1007/978-3-319-05681-4_7

    DOI: 10.1007/978-3-319-05681-4_7

    2013

    Birationally rigid complete intersections of quadrics and cubics (Journal article)

    Pukhlikov, A. V. (2013). Birationally rigid complete intersections of quadrics and cubics. Izvestiya: Mathematics, 77(4), 795-845. doi:10.1070/IM2013v077n04ABEH002661

    DOI: 10.1070/IM2013v077n04ABEH002661

    Birational rigidity of Fano complete intersections (Journal article)

    Pukhlikov, A. V. (2013). Birational rigidity of Fano complete intersections. Doklady Mathematics, 87(1), 34-35. doi:10.1134/s1064562413010134

    DOI: 10.1134/s1064562413010134

    Birationally rigid Fano varieties (Book)

    Pukhlikov, A. V. (n.d.). Birationally rigid Fano varieties. Retrieved from http://arxiv.org/abs/math/0310267v1

    2012

    K-trivial structures on Fano complete intersections (Journal article)

    Pukhlikov, A. V. (2012). K-trivial structures on Fano complete intersections. Mathematical Notes, 91(3-4), 568-574. doi:10.1134/s0001434612030315

    DOI: 10.1134/s0001434612030315

    On the multiplicity of solutions of a system of algebraic equations (Journal article)

    Pukhlikov, A. V. (2012). On the multiplicity of solutions of a system of algebraic equations. Proceedings of the Steklov Institute of Mathematics, 276(1), 234-249. doi:10.1134/s0081543812010208

    DOI: 10.1134/s0081543812010208

    2011

    Birationally rigid Fano complete intersections. II (Journal article)

    Pukhlikov, A. V. (2011). Birationally rigid Fano complete intersections. II. arXiv:math.AG, 10 pages.

    2010

    Birationally rigid varieties. II. Fano fibre spaces (Journal article)

    Pukhlikov, A. V. (2010). Birationally rigid varieties. II. Fano fibre spaces. Russian Mathematical Surveys, 65(6), 1083-1171. doi:10.1070/rm2010v065n06abeh004716

    DOI: 10.1070/rm2010v065n06abeh004716

    Birational geometry of singular Fano double spaces of index two (Journal article)

    Pukhlikov, A. V. (n.d.). Birational geometry of singular Fano double spaces of index two. Retrieved from http://arxiv.org/abs/1912.04817v1

    Birational geometry of Fano double spaces of index two (Journal article)

    Pukhlikov, A. (2010). Birational geometry of Fano double spaces of index two. Izvestiya: Mathematics, 74(5), 925-991. doi:10.1070/IM2010v074n05ABEH002512

    DOI: 10.1070/IM2010v074n05ABEH002512

    On the self-intersection of a movable linear system (Journal article)

    Pukhlikov, A. V. (2010). On the self-intersection of a movable linear system. Journal of Mathematical Sciences, 164(1), 119-130. doi:10.1007/s10958-009-9741-3

    DOI: 10.1007/s10958-009-9741-3

    The rationality problem and birational rigidity (Chapter)

    Pukhlikov, A. V. (2010). The rationality problem and birational rigidity. In F. A. Bogomolov, Y. Tchinkel, H. Bass, J. Oesterle, & A. Weinstein (Eds.), The rationality problem (Vol. 282, pp. 275-311). Boston - Basel - Berlin: Birkhauser.

    2009

    Singularities of algebraic subvarieties and problems of birational geometry (Journal article)

    Pukhlikov, A. V. (2009). Singularities of algebraic subvarieties and problems of birational geometry. Proceedings of the Steklov Institute of Mathematics, 267(1), 235-247. doi:10.1134/s0081543809040191

    DOI: 10.1134/s0081543809040191

    Birational geometry of singular Fano varieties (Journal article)

    Pukhlikov, A. V. (2009). Birational geometry of singular Fano varieties. Proceedings of the Steklov Institute of Mathematics, 264(1), 159-177. doi:10.1134/s0081543809010180

    DOI: 10.1134/s0081543809010180

    Birational Geometry of Algebraic Varieties with a Pencil of Fano Cyclic Covers (Journal article)

    Pukhlikov, A. V. (2009). Birational Geometry of Algebraic Varieties with a Pencil of Fano Cyclic Covers. Pure and Applied Mathematics Quarterly, 5(2), 641-700. doi:10.4310/pamq.2009.v5.n2.a4

    DOI: 10.4310/pamq.2009.v5.n2.a4

    2008

    Birational geometry of Fano double covers (Journal article)

    Pukhlikov, A. V. (2008). Birational geometry of Fano double covers. Sbornik: Mathematics, 199(8), 1225-1250. doi:10.1070/sm2008v199n08abeh003960

    DOI: 10.1070/sm2008v199n08abeh003960

    2007

    Birationally rigid varieties. I. Fano varieties (Journal article)

    Pukhlikov, A. V. (2007). Birationally rigid varieties. I. Fano varieties. Russian Mathematical Surveys, 62(5).

    Explicit examples of birationally rigid Fano varieties (Journal article)

    Pukhlikov, A. V. (2007). Explicit examples of birationally rigid Fano varieties. Moscow Mathematical Journal, 7(3), 543-560.

    Fano direct products as rationally connected fibrations (Journal article)

    Pukhlikov, A. V. (2007). Fano direct products as rationally connected fibrations. Journal of Mathematical Sciences, 140(2), 303-320.

    Quadratic methods in optimal control theory and systems theory (Chapter)

    Pukhlikov, A. V. (2007). Quadratic methods in optimal control theory and systems theory. In S. K. Korovin, & S. V. Emel'yanov (Eds.), Non-Linear Dynamics and Control (Vol. 5, pp. 69-98). Moscow: FIZMATLIT.

    2006

    Birational geometry of algebraic varieties with a pencil of Fano complete intersections (Journal article)

    Pukhlikov, A. V. (n.d.). Birational geometry of algebraic varieties with a pencil of Fano complete intersections. Retrieved from http://arxiv.org/abs/math/0511090v1

    Birationally rigid varieties with a pencil of Fano double covers. I (Journal article)

    Pukhlikov, A. V. (n.d.). Birationally rigid varieties with a pencil of Fano double covers. I. Retrieved from http://arxiv.org/abs/math/0310270v1

    2005

    Birational geometry of Fano direct products (Journal article)

    Pukhlikov, A. V. (n.d.). Birational geometry of Fano direct products. doi:10.1070/IM2005v069n06ABEH002300

    DOI: 10.1070/IM2005v069n06ABEH002300

    Geometry of Discontinuous Systems near a Manifold of Singularities of Third Order (Journal article)

    Pukhlikov, A. V. (2005). Geometry of Discontinuous Systems near a Manifold of Singularities of Third Order. Differential Equations, 41(12), 1710-1716. doi:10.1007/s10625-006-0007-2

    DOI: 10.1007/s10625-006-0007-2

    Birationally rigid varieties with a pencil of Fano double covers. III (Journal article)

    Pukhlikov, A. V. (n.d.). Birationally rigid varieties with a pencil of Fano double covers. III. doi:10.1070/SM2006v197n03ABEH003761

    DOI: 10.1070/SM2006v197n03ABEH003761

    Birationally rigid direct Fano products (Journal article)

    Pukhlikov, A. V. (2005). Birationally rigid direct Fano products. Doklady: Mathematics, 401(2), 163-165.

    2004

    Birationally rigid varieties with a pencil of Fano double covers. II (Journal article)

    Pukhlikov, A. V. (n.d.). Birationally rigid varieties with a pencil of Fano double covers. II. doi:10.1070/SM2004v195n11ABEH000861

    DOI: 10.1070/SM2004v195n11ABEH000861

    Birationally rigid Fano cyclic covers (Journal article)

    Pukhlikov, A. V. (n.d.). Birationally rigid Fano cyclic covers. Retrieved from http://arxiv.org/abs/math/0411198v1

    Birationally rigid varieties with a pencil of double Fano covers. I (Journal article)

    Pukhlikov, A. V. (2004). Birationally rigid varieties with a pencil of double Fano covers. I. Sbornik: Mathematics, 195(7), 1039-1071. doi:10.1070/sm2004v195n07abeh000837

    DOI: 10.1070/sm2004v195n07abeh000837

    2003

    Birationally rigid iterated Fano double covers (Journal article)

    Pukhlikov, A. V. (n.d.). Birationally rigid iterated Fano double covers. Izvestiya: Mathematics. 67 (2003), no. 3, 555-596. doi:10.1070/IM2003v067n03ABEH000438

    DOI: 10.1070/IM2003v067n03ABEH000438

    2002

    Birationally rigid Fano hypersurfaces (Journal article)

    Pukhlikov, A. V. (n.d.). Birationally rigid Fano hypersurfaces. doi:10.1070/IM2002v066n06ABEH000413

    DOI: 10.1070/IM2002v066n06ABEH000413

    Birationally rigid Fano hypersurfaces with isolated singularities (Journal article)

    Pukhlikov, A. V. (n.d.). Birationally rigid Fano hypersurfaces with isolated singularities. doi:10.1070/SM2002v193n03ABEH000640

    DOI: 10.1070/SM2002v193n03ABEH000640

    2001

    Birationally rigid Fano complete intersections (Journal article)

    Pukhlikov, A. V. (2001). Birationally rigid Fano complete intersections. Journal für die reine und angewandte Mathematik (Crelles Journal), 2001(541). doi:10.1515/crll.2001.095

    DOI: 10.1515/crll.2001.095

    (Journal article)

    Pukhlikov, A. V. (2001). Unknown Title. Differential Equations, 37(3), 377-400. doi:10.1023/a:1019246616381

    DOI: 10.1023/a:1019246616381

    1998

    Essentials of the method of maximal singularities (Journal article)

    Pukhlikov, A. V. (n.d.). Essentials of the method of maximal singularities. Retrieved from http://arxiv.org/abs/math/9806138v1

    1996

    Birational automorphisms of algebraic varieties with a pencil of cubic surfaces (Journal article)

    Pukhlikov, A. V. (n.d.). Birational automorphisms of algebraic varieties with a pencil of cubic surfaces. Retrieved from http://arxiv.org/abs/alg-geom/9611009v1