The KSBA compactification for the moduli space of degree two \(K3\) pairs

DOI10.4171/JEMS/589zbMATH Open1375.14126arXiv1205.3144OpenAlexW2963545755MaRDI QIDQ252670

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Publication date: 3 March 2016

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Abstract: Inspired by the ideas of the minimal model program, Shepherd-Barron, Koll'ar, and Alexeev have constructed a geometric compactification for the moduli space of surfaces of log general type. In this paper, we discuss one of the simplest examples that fits into this framework: the case of pairs (X,H) consisting of a degree two K3 surface X and an ample divisor H. Specifically, we construct and describe explicitly a geometric compactification

for the moduli of degree two K3 pairs. This compactification has a natural forgetful map to the Baily-Borel compactification of the moduli space

F_{2}

of degree two K3 surfaces. Using this map and the modular meaning of

, we obtain a better understanding of the geometry of the standard compactifications of

F_{2}

.

Full work available at URL: https://arxiv.org/abs/1205.3144

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