Algebraic Geometry Seminar | Samuel Grushevsky (Stony Brook University)

Title: Non-isomorphic compactifications of moduli of cubic surfaces and threefolds

Abstract: The moduli space of cubic surfaces and cubic threefolds have different reincarnations in algebraic geometry, and can be compactified via geometric invariant theory or via looking at the minimal compactification of their ball quotient models. These compactifications are singular, and resolved respectively by the Kirwan blowup and the toroidal compactification. We show that these smooth compactifications have equal Betti numbers, but are non-isomorphic. Based on joint works with Casalaina-Martin, Hulek, and Laza.

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