椭圆型K3曲面的紧模

Geometry & Topology Pub Date : 2019-02-27 DOI:10.2140/gt.2023.27.1891

Kenneth Ascher, Dori Bejleri

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引用次数: 12

摘要

利用最小模型程序中的工具构造了椭圆型K3曲面空间的各种模紧化，并明确地描述了由其边界参数化的曲面。我们构造的紧化的粗糙空间承认Satake-Baily-Borel紧化的态射。最后，我们证明了我们的一个空间是光滑的，而粗糙的空间是具有选定纤维的weerstrass K3曲面对的GIT商。

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Compact moduli of elliptic K3 surfaces

We construct various modular compactifications of the space of elliptic K3 surfaces using tools from the minimal model program, and explicitly describe the surfaces parametrized by their boundaries. The coarse spaces of our constructed compactifications admit morphisms to the Satake-Baily-Borel compactification. Finally, we show that one of our spaces is smooth with coarse space the GIT quotient of pairs of Weierstrass K3 surfaces with a chosen fiber.

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Geometry & Topology

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