Kodaira Workshop

This is a weekend workshop in Algebraic Geometry, and coincides with the birthday
of Kunihiko KodairaThe workshop is sponsored by the Loughborough University

Friday 15th March -- Saturday 16th March, 2019

Registration Form (Deadline: March 10th)

Hamid Ahmadinezhad (Loughborough)
Ivan Cheltsov (Edinburgh)

  • Caucher Birkar (Cambridge)
  • Soheyla Feyzbakhsh (Imperial College London)
  • Alexander Kuznetsov (Steklov Institute and HSE)
  • Evgeny Shinder (Sheffield) 
  • Konstantin Shramov (Steklov Institute and HSE)
  • Hendrik Süß (Manchester)
  • Gerard van der Geer (Amsterdam)


 Friday March 15th
all talks in SCH105   
 Saturday March 16th
all talks in SCH101

 13:30 - 14:30
10:30 - 11:30
 14:30 - 15:00
12:00 - 13:00
van der Geer
 15:00 - 16:00
13:00 - 14:30
Lunch & Coffee
 16:15 - 17:15
14:30 - 15:30
15:45 - 16:45

Titles and Abstracts:

Title: Log Calabi-Yau fibrations
Abstract: In this talk I will introduce the notion of log Calabi-Yau fibrations
and discuss how it unifies various concepts of birational geometry. Next I
will describe some recent results and some open problems in this direction.

Title: Wall-crossing and Brill-Noether theory 
Abstract: I will first introduce a new upper bound for the number of global
sections of sheaves on K3 surfaces which is obtained via wall-crossing
with respect to Bridgeland stability conditions.  Then I will explain some
of its results including verification of Mukai's program to reconstruct a K3
surface from a curve on that surface and computing higher-rank Clifford
indices of curves on K3 surfaces.  

Title: Rationality of prime Fano 3-folds over nonclosed fields
Abstract: In the talk I will discuss rationality questions for forms of classical
prime Fano 3-folds over nonclosed fields of characteristic 0.

Title: Stable birational types of Fano hypersurfaces of high degree
Abstract: It is known by the work of Kollar, Totaro and Schreieder that
very general Fano hypersurfaces of high degree are not stably rational.
In this talk I explain how to apply the specialization for the Grothendieck
ring of varieties in order to prove that very general such hypersurfaces
are not stably birational to each other.

Title: Singular Veronese double cones
Abstract: Varieties with the largest possible number of isolated 
singularities in a given deformation family often have nice geometric
properties. For instance, the Segre cubic, which is the unique cubic
threefold with 10 nodes, is known to be related to certain moduli spaces
of abelian surfaces. Del Pezzo threefolds of degree 2 with maximal
number of isolated singularities are double solids branched in Kummer 
quartic surfaces.
In my talk I will describe the geometry of del Pezzo threefolds of 
degree 1 (also known as Veronese double cones) with the maximal 
possible number of isolated singularities. Such varieties are nodal and 
have 28 singular points. They are in one-to-one correspondence with 
smooth plane quartics, and much of their properties can be recovered 
from the properties of these quartics. The talk is based on a joint work
in progress with H. Ahmadinezhad, I. Cheltsov and J. Park.

Title: Stability of tangent bundles on toric surfaces
Abstract: For a smooth rational surfaces one may ask under which
conditions there is a polarisation, such that the tangent bundle becomes
stable. In this talk I will present a complete answer to this question in
the toric case. If time permits I will also discuss some higher dimensional
toric examples.
This is joint work with Milena Hering and Benjamin Nill

van der Geer
Title: Algebraic curves and modular forms of degree two and three
Abstract: Siegel modular forms of degree 2 (resp. 3) are intimately
connected with moduli of curves of genus 2 (resp. 3). We show that
classical invariant theory yields an effective way to construct modular
forms and then give attention to modular forms of degree 2 and low
weight. This is joint work with Clery and Faber.