Steven Lu (UQAM)
Title: Hyperkahler manifolds dominable by C^n, Part II
Abstract: In this second talk, I will review the proof of my main dominability results obtained jointly with Greg Buzzard on elliptic K3 surfaces before delving into their higher dimensional analog, the Lagrangian fibered hyperkahler manifolds. Related work joint also with Verbitsky and Bogomolov will be mentioned as backdrop and motivation from the perspective of (anti)hyperbolicity, holomorphic analog of rational connectedness (and of unirationality at times) in the Ricci flat setting. We will describe briefly the two principal classical series of examples of hyperkahler manifold, the Hilbert schemes of points on K3 (and abelian) surfaces and the generalized Kummer varieties in order to talk about their homomorphic dominability by C^n. We will also show the dominability of Lagrangian fibered hyperkahler manifolds in dimension four, and in higher dimension, of those that are either doubly so fibered or satisfy the usual ansatz. We will elucidate further the geometry and their behaviour in moduli space as possible prelude to
generalizing these partial results time permitting.
In person at UQAM PK-5675
or online at Zoom meeting 86352363947