Moduli Day (January 30, 2020)
The talks will all take place on Thursday January 30, 2020, in room 02.06.11. That is room 11 on the second floor of part 6 of the department of Mathematics of the TUM at Boltzmannstrasse 3, 85748 Garching, München.
There will be coffee provided between the talks.
Speakers and Schedule
Gavril Farkas (10:00 - 11:00)
Title: Moduli of K3 surfaces via cubic 4-folds
Abstract: In a celebrated series of papers, Mukai established structure theorems for polarized K3 surfaces of all genera g<21, with the exception of the case g=14. Using the identification between certain moduli spaces of polarized K3 surfaces and the moduli space of special cubic fourfolds of given discriminant, we discuss a novel approach to moduli spaces of K3 surfaces. As an application, we establish the rationality of the universal K3 surface of these genus 14 and 22. This is joint work with A. Verra.
Georg Oberdieck (11:30 - 12:30)
Title: Motivic decompositions of the Hilbert scheme of points of a K3 surface
Abstract: I will discuss joint work with Andrei Negut and Qizheng Yin in which we construct a multiplicative Chow-Künneth decomposition of the Hilbert scheme of points on a K3 surface. This is parallel to the case of abelian varieties where such a decomposition is induced by the Fourier-Mukai transform.
Ana-Maria Castravet (14:00 - 15:00)
Title: Exceptional collections on moduli spaces of stable rational curves
Abstract: A question of Orlov is whether the derived category of the Grothendieck-Knudsen moduli space M(0,n) of stable, rational curves with n markings admits a full, strong, exceptional collection that is invariant under the action of the symmetric group S_n. A consequence of the conjecture is the existence of an S_n invariant basis in the cohomology of M(0,n) (in particular, the S_n representation given by the cohomology is a permutation representation). I will present joint work with Jenia Tevelev towards answering this question.
Rahul Pandharipande (15:30 - 16:30)
Title: Descendents for stable pairs on 3-folds
Abstract: Descendent classes on moduli spaces of sheaves are defined via the Chern characters of the universal sheaf. I will present several conjectures and results concerning stable pairs descendent invariants for 3-folds: rationality of generating functions, functional equations, cobordism classes, and Virasoro constraints.