Algebraic Geometry

Algebraic Geometry Seminars

Seminar details for 2016 onwards can be found at the Pure Mathematics Seminars page


Tuesday 15th December 2015, 17:00 - 18:00, Room MATH-104
Classification of degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups, II - Viacheslav Nikulin (Steklov Institute, Moscow)

Abstract: We prove the main Conjecture of our paper: Part I, Izvestia:Mathematics 2015, arXiv:1403.6061. Further, we apply these results to classification of degenerations of codimension one of Kahlerian K3 surfaces with finite symplectic automorphism groups. By classfication, we understand an enumeration of connected components of the corresponding moduli. The report follows to my preprint arXiv:1504.00326 (October 2015).


Tuesday 1st December 2015, 17:00 - 18:00, Room MATH-104
Rationally connected non Fano type varieties - Igor Krylov (University of Edinburgh)

Abstract: The class of varieties of Fano type is a generalization of Fano varieties which is very well behaved under the MMP. It is known that all varieties of Fano type are rationally connected. The converse is true in a sense in dimension 2. I will give counterexamples to the converse statement in dimension 3 and higher. I will use the techniques of birational rigidity and MMP.


Friday 27th November 2015, 17:00 - 18:00, Room MATH-104
Open problems about ample divisors on del Pezzo surfaces - Ivan Cheltsov


Monday 21st September 2015, 10:00 - 15:30, Room MATH-029
One day conference - "Moduli spaces and their applications"
Organiser: Nicola Pagani


Friday 12th June 2015, 15:00, Room 105
Irrational singular quartic double solids - Costya Shramov

Costya will speak about irrationality results for nodal quartic double solids that can be obtained using conic bundle structures and intermediate Jacobians. This is a joint work with I. Cheltsov and V. Przyjalkowski.


Friday 24th April and Friday 1st May 2015, 17:00, Room 104
Birationally rigid Fano fibre spaces - Aleksandr Pukhlikov

The aim of the talks is to review the known results on birational rigidity of Fano fibre spaces and to explain my last theorem on birational rigidity of Fano-Mori fibre spaces over a higher-dimensional base.


Tuesday 10th, 17th, 24th March 2015, 16:00, Room 104
Intersection theory on the universal compactified Jacobian: the theta divisor - Nicola Pagani

The moduli space of line bundles on a curve can be non-compact even when the worst singularities of the curve are nodes. A natural compactification is obtained by adding stable rank-1 torsion-free sheaves: such compactification depends on the choice of a polarization on the nodal curve. Similarly, when compactifying the universal Jacobian over the moduli space of stable curves, one obtains a family of compact birational moduli spaces that depend on a polarization parameter. In this talk I will present a wall-crossing formula that describes how the theta divisor varies as a function of this parameter. This is a joint work with Jesse Kass (South Carolina).


Tuesday 3rd March 2015, 16:00, Room 104
Topology of Hilbert schemes of points on orbifolds - Paul Johnson

The Hilbert scheme of n points on a complex surface is a smooth manifold of dimension 2n. The topology of these manifolds have beautiful structure related to physics, representation theory, and combinatorics. Hilbert schemes of points on C^2/G, for G a finite group, are also smooth, and when G is abelian their topology is encoded in the combinatorics of partitions. When G is a subgroup of SL_2, the topology and combinatorics of the situation are well understood, but much less is known for general G. We present some conjectures and partial results for the case of general abelian G, but much of our time will be spent reviewing the basics.