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Titlebook: Birational Geometry of Hypersurfaces; Gargnano del Garda, Andreas Hochenegger,Manfred Lehn,Paolo Stellari Book 2019 Springer Nature Switze

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Hodge Theory of Cubic Fourfolds, Their Fano Varieties, and Associated K3 Categoriesge structures that come naturally associated with a cubic fourfold. The emphasis is on the Hodge and lattice theoretic aspects with many technical details worked out explicitly. More geometric or derived results are only hinted at.
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Lectures on Non-commutative K3 Surfaces, Bridgeland Stability, and Moduli Spacesm 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 conjec
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