Compact K3 moduli

Abstract: The moduli space of polarized K3 surfaces is a non-compact quotient of a symmetric space by an arithmetic group. In this capacity, it has an infinite class of combinatorially-defined "semitoroidal compactifications." I will discuss joint work with Valery Alexeev that sometimes semitoroidal compactifications have geometric meaning: they parameterize "stable K3 surfaces" in a way similar to how the Deligne-Mumford compactification of curves parameterizes "stable curves." Inspired by ideas from mirror symmetry, the semifan of such a compactification can sometimes be computed, using symplectic and integral-affine geometry.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

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