Lectures on Non-commutative K3 Surfaces, Bridgeland Stability, and Moduli Spaces

By Emanuele Macrì, P. Stellari. Lecture Notes of the Unione Matematica Italiana, 2018

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We survey the basic theory of non-commutative K3 surfaces, with a particular emphasis to the ones arising from cubic fourfolds. We focus on the problem of constructing Bridgeland stability conditions on these categories and we then investigate the geometry of the corresponding moduli spaces of stable objects. We discuss a number of consequences related to cubic fourfolds including new proofs of the Torelli theorem and of the integral Hodge conjecture, the extension of a result of Addington and Thomas and various applications to hyperkahler manifolds.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9a94ebd43e678e7965da0725370457af559f6669