JournalsjemsVol. 18, No. 2pp. 225–279

The KSBA compactification for the moduli space of degree two KK3 pairs

  • Radu Laza

    Stony Brook University, USA
The KSBA compactification for the moduli space of degree two $K$3 pairs cover
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Abstract

Inspired by the ideas of the minimal model program, Shepherd-Barron, Kollár, 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)(X,H) consisting of a degree two K3K3 surface XX and an ample divisor HH. Specifically, we construct and describe explicitly a geometric compactification P2\overline{\mathcal P}_2 for the moduli of degree two KK3 pairs. This compactification has a natural forgetful map to the Baily–Borel compactification of the moduli space F2\mathcal F_2 of degree two KK3 surfaces. Using this map and the modular meaning of P2\overline{\mathcal P}_2, we obtain a better understanding of the geometry of the standard compactifications of F2\mathcal F_2.

Cite this article

Radu Laza, The KSBA compactification for the moduli space of degree two KK3 pairs. J. Eur. Math. Soc. 18 (2016), no. 2, pp. 225–279

DOI 10.4171/JEMS/589