# The KSBA compactification for the moduli space of degree two $K3$ pairs

Journal of the European Mathematical Society (2016)

- Volume: 018, Issue: 2, page 225-279
- ISSN: 1435-9855

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topLaza, Radu. "The KSBA compactification for the moduli space of degree two $K3$ pairs." Journal of the European Mathematical Society 018.2 (2016): 225-279. <http://eudml.org/doc/277263>.

@article{Laza2016,

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 $(X,H)$ consisting of a degree two $K3$ surface $X$ and an ample divisor $H$. Specifically, we construct and describe explicitly a geometric compactification $\bar\{P\}_2$ for the moduli of degree two $K3$ pairs. This compactification has a natural forgetful map to the Baily–Borel compactification of the moduli space $\mathcal \{F\}_2$ of degree two $K3$ surfaces. Using this map and the modular meaning of $\bar\{P\}_2$, we obtain a better understanding of the geometry of the standard compactifications of $_2$.},

author = {Laza, Radu},

journal = {Journal of the European Mathematical Society},

keywords = {$K3$ surfaces; moduli space of $K3$ surfaces; KSBA; surfaces; moduli space of surfaces; KSBA},

language = {eng},

number = {2},

pages = {225-279},

publisher = {European Mathematical Society Publishing House},

title = {The KSBA compactification for the moduli space of degree two $K3$ pairs},

url = {http://eudml.org/doc/277263},

volume = {018},

year = {2016},

}

TY - JOUR

AU - Laza, Radu

TI - The KSBA compactification for the moduli space of degree two $K3$ pairs

JO - Journal of the European Mathematical Society

PY - 2016

PB - European Mathematical Society Publishing House

VL - 018

IS - 2

SP - 225

EP - 279

AB - 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 $(X,H)$ consisting of a degree two $K3$ surface $X$ and an ample divisor $H$. Specifically, we construct and describe explicitly a geometric compactification $\bar{P}_2$ for the moduli of degree two $K3$ pairs. This compactification has a natural forgetful map to the Baily–Borel compactification of the moduli space $\mathcal {F}_2$ of degree two $K3$ surfaces. Using this map and the modular meaning of $\bar{P}_2$, we obtain a better understanding of the geometry of the standard compactifications of $_2$.

LA - eng

KW - $K3$ surfaces; moduli space of $K3$ surfaces; KSBA; surfaces; moduli space of surfaces; KSBA

UR - http://eudml.org/doc/277263

ER -

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