Geometric Methods in Representation Theory – Giacomo Nanni (Universita di Bologna)

Lagrangian Planes on Kummer-Type Manifolds

Abstract: The birational geometry of K3 surfaces can be understood through their intersection theory, and Hassett and Tschinkel initiated a program to achieve a similar understanding for their higher-dimensional analogs: irreducible holomorphic symplectic (IHS) manifolds. Recent developments in Bridgeland stability theory have brought new insights to this problem. In this talk, I will provide a brief introduction to IHS manifolds, followed by an overview of the theory of moduli spaces of Bridgeland-stable objects on K3 and abelian surfaces. I will then present a characterization of the homology class of lines contained in Lagrangian planes within IHS manifolds of K3^[n] or generalized Kummer type.

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