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Title:
K-moduli of curves on a quadric surface and K3 surfaces
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Abstract:
By regarding a (d,d) curve C on a quadric surface as a log Fano pair (P1xP1, aC), where a is a rational number, one can use K moduli to study a family of compactifications of the moduli spaces of these curves as a varies. Of particular interest is the case d = 4: a general hyperellipic degree 4 K3 surface is a double cover branched over such a curve. In this case, we show that K stability provides a natural way to interpolate between the GIT moduli space of (4,4) curves and the Baily-Borel compactification of the K3 surfaces. Furthermore, Laza and O’Grady have shown how to interpolate between these moduli spaces via a series of explicit VGIT wall crossings, and we show that these VGIT walls coincide exactly with the K moduli wall crossings. This is joint work with Kenneth Ascher and Yuchen Liu.
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