K-MODULI OF CURVES ON A QUADRIC SURFACE AND K3 SURFACES
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Abstract We show that the K-moduli spaces of log Fano pairs $\left(\mathbb {P}^1\times \mathbb {P}^1, cC\right)$ , where C is a $(4,4)$ curve and their wall crossings coincide with the VGIT quotients of $(2,4)$ , complete intersection curves in $\mathbb {P}^3$ . This, together with recent results by Laza and O’Grady, implies that these K-moduli spaces form a natural interpolation between the GIT moduli space of $(4,4)$ curves on $\mathbb {P}^1\times \mathbb {P}^1$ and the Baily–Borel compactification of moduli of quartic hyperelliptic K3 surfaces.
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2000 ◽
Vol 128
(1)
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pp. 79-86
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2003 ◽
Vol 14
(08)
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pp. 837-864
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2005 ◽
Vol 16
(01)
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pp. 13-36
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