Non-commutative abelian surfaces and generalized Kummer varieties

Abstract: A hyperkaehler manifold is a compact complex simply connected Kaehler manifold whose space of holomorphic two-forms is generated by a symplectic form, unique up to scalar multiplication. Together with complex tori and irreducible Calabi--Yau manifolds, they are building blocks for compact Kaehler manifolds with trivial first Chern class. In dimension two hyperkaehler manifolds are K3 surfaces, while finding examples in higher dimensions is a challenging problem. In this talk we will construct new families of hyperkahler manifolds of generalized Kummer type via moduli spaces of stable objects in a noncommutative deformation of the bounded derived category of an abelian surface. This work in progress is joint with Arend Bayer, Alex Perry and Xiaolei Zhao.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides )

Comments: https://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09

Meeting ID: 918 7552 8987 Password: LAGOON

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

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