# Moduli spaces of quartic hyperelliptic K3 surfaces via K-stability

### Yuchen Liu (Yale)

29-May-2020, 17:45-18:45 (8 months ago)

Abstract: A general polarized hyperelliptic K3 surfaces of degree 4 is a double cover of $\mathbf{P }^ 1 \times \mathbf{P}^1$ branched along a bidegree $(4,4)$ curve. Classically there are two compactifications of their moduli spaces: one is the GIT quotient of $(4,4)$ curves, the other is the Baily-Borel compactification of their periods. We show that K-stability provides a natural modular interpolation between these two compactifications. This provides a new aspect toward a recent result of Laza-O'Grady. Based on joint work in progress with K. Ascher and K. DeVleming.

algebraic geometry

Audience: researchers in the topic

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