ICTP Mathematics Seminar - Wednesday, 23 October 2024, at 11:00 - VENUE: Luigi Stasi Seminar Room - Yulieth Prieto Montanez

[ICTP Math Section]

*ICTP Mathematics Seminar
*

Wednesday, 23 October 2024, at 11:00



VENUE: ICTP Leonardo Building - Luigi Stasi Seminar Room


Speaker: Yulieth Prieto Montanez (Pontificia Universidad Católica de Chile)

Title: *Projective Hyperkähler Manifolds with Large Picard Number *

Abstract:

Compact Hyperkähler manifolds (also known as IHS) are notable Kähler 
manifolds renowned for their rich and intriguing geometry. Using 
classical results from quadratic forms and advance methods from 
Bridgeland stability conditions, we will show that any projective 
Hyperkähler manifold (deforming to the Hilbert scheme of n points on a 
K3 surface) with a Picard number at least 4 is always isomorphic to a 
moduli space of (twisted) stable sheaves on a K3 surface.
We will also discuss exampleswith Picard numbers less than 4, including 
cases that are not birational to a moduli space of twisted sheaves on a 
K3 surface. These examples reveal connections to an open problem in 
algebraic geometry regarding therationality of cubic fourfolds.