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Categorical Torelli for cyclic covers

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If you have a question about this talk, please contact Dhruv Ranganathan .

Since any Fano variety can be recovered from its derived category up to isomorphism, we ask whether less information determines the variety – this is called a categorical Torelli question. In this talk, we consider an n-fold cover X → Y ramified in a divisor Z. The cyclic group of order n acts on X. We study how a certain subcategory of Db(X) (the Kuznetsov component) behaves under this group action. We combine this with techniques from topological K-theory and Hodge theory to prove that this subcategory determines X for two new classes of Fano threefolds which arise as double covers of (weighted) projective spaces. This is joint work with Augustinas Jacovskis and Franco Rota (arXiv:2310.13651).

This talk is part of the Algebraic Geometry Seminar series.

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