K-stability and birational geometry of moduli spaces of quartic K3 surfaces

Abstract: Recently it has been shown that K-stability provides well-behaved moduli spaces of Fano varieties and log Fano pairs, and allows one to naturally interpolate between other geometric compactifications. I will discuss the picture for quartic K3 surfaces, relating compactifications coming from geometric invariant theory (GIT), Hodge theory, and K-stability via wall crossings in K-moduli. This is joint work with Kenneth Ascher and Yuchen Liu.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

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