K-MODULI OF CURVES ON A QUADRIC SURFACE AND K3 SURFACES
K-MODULI OF CURVES ON A QUADRIC SURFACE AND K3 SURFACES
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DOI：
10.1017/s1474748021000384
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发表时间：
2020-06
影响因子：
0.9
通讯作者：
Kenneth Ascher;Kristin DeVleming;Yuchen Liu
中科院分区：
文献类型：
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作者：
Kenneth Ascher;Kristin DeVleming;Yuchen Liu
**摘要**：我们证明了对数法诺对\((\mathbb {P}^1\times \mathbb {P}^1, cC)\)的K - 模空间（其中\(C\)是一条\((4, 4)\)曲线）及其壁交叉与\(\mathbb {P}^3\)中\((2, 4)\)型完全交曲线的VGIT商一致。结合拉扎（Laza）和奥格雷迪（O’Grady）最近的研究成果，这意味着这些K - 模空间在\(\mathbb {P}^1\times \mathbb {P}^1\)上\((4, 4)\)曲线的GIT模空间与四次超椭圆K3曲面模空间的贝利 - 博雷尔（Baily–Borel）紧化之间构成了一种自然的插值。
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.