Prof. Dr. Junliang Shen (Yale University)
Algebraic cycles on hyper-Kähler varieties via hyperholomorphic bundles abstract
Abstract:
Hyper-Kähler varieties are higher dimensional analogs of K3 surfaces. Conjectures of Beauville and Voisin predict that the Chow ring of a hyper-Kähler variety "behaves like" the Chow ring of an abelian variety. The first part of the talk is to discuss a proposal explaining this phenomenon for hyper-Kähler varieties of K3[n]-type, where our new tools are the hyperholomorphic bundles constructed recently by Markman. In the second part, I will discuss applications of these ideas to the Orlov conjecture (and beyond) for certain hyper-Kähler varieties of K3[n]-type. Based on joint work in progress with Davesh Maulik and Qizheng Yin.
16:00 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1