Program - December 18, 2017 (Aula C, second floor)
You can download the poster and the program.
10:00-10:50
Fabio Tanturri
Orbital degeneracy loci
Abstract:
Let s be a section of a vector bundle E on an algebraic variety X. We can look at the locus of points x in X where s degenerates, i.e. s(x) belongs to a fixed subvariety of the total space of E defined fiberwise; this locus, which we call orbital degeneracy locus, generalizes for instance the classical degeneracy locus of a morphism between two vector bundles.
In this talk I will introduce some techniques to understand and study this new class of objects. With such techniques, we can produce several interesting examples of projective varieties; in particular, I will exhibit some constructions for varieties with trivial canonical bundle. This is part of a joint project in collaboration with Vladimiro Benedetti, Sara Angela Filippini, and Laurent Manivel.
11:00-11:50
Alberto Cattaneo
Automorphisms of hyperkähler manifolds: a classification
Abstract:
Boissière, Camere and Sarti provided a classification of non-symplectic automorphisms of prime order acting on irreducible holomorphic symplectic fourfolds deformation equivalent to the Hilbert scheme of two points on a K3 surface. This classification relies on the study of the invariant lattice of the automorphism (and its orthogonal complement) inside the second cohomology group with integer coefficients, equipped with the Beauville-Bogomolov-Fujiki quadratic form. I will report on a joint work in progress with Camere about extending this classification to manifolds of higher dimension, which are still deformations of Hilbert schemes of points on K3 surfaces. I will also discuss some explicit ways to produce automorphisms of such varieties.
14:00-14:50
Eleonora Anna Romano
An overview of Fano conic bundles
Abstract:
Given a smooth, complex, projective and Fano variety of arbitrary dimension, a conic bundle of such a variety is a fiber-type contraction with one-dimensional fibers. The purpose of this talk is to give an overview of such morphisms, and to discuss some recent results which allow to deduce many geometric properties about the involved varieties. Using these results, we focus on some applications and new examples of Fano conic bundles in high dimension. Time permitting, some recent developments about conic bundles of Fano 4-folds are presented.
15:00-15:50
Soheyla Feyzbakhsh
Reconstructing a K3 surface from a curve via wall-crossing
Abstract:
Mukai has introduced a geometric program to reconstruct a K3 surface from a curve on that surface. The idea is to first consider a Brill-Noether locus of vector bundles on the curve. Then the K3 surface containing the curve can be obtained uniquely as a Fourier-Mukai partner of the Brill-Noether locus. In this talk, I will explain how wall-crossing with respect to Bridgeland stability conditions implies that the Mukai's strategy works for curves of genus greater than 12 or genus 11.