The KSBA compactification for the moduli space of degree two 3 pairs

  • Radu Laza

    Stony Brook University, USA

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 consisting of a degree two surface and an ample divisor . Specifically, we construct and describe explicitly a geometric compactification for the moduli of degree two 3 pairs. This compactification has a natural forgetful map to the Baily–Borel compactification of the moduli space of degree two 3 surfaces. Using this map and the modular meaning of , we obtain a better understanding of the geometry of the standard compactifications of .

Cite this article

Radu Laza, The KSBA compactification for the moduli space of degree two 3 pairs. J. Eur. Math. Soc. 18 (2016), no. 2, pp. 225–279

DOI 10.4171/JEMS/589