Compact moduli of elliptic K3 surfaces

Ascher, Kenneth¹ ; Bejleri, Dori²

¹ Department of Mathematics, University of California, Irvine, Irvine, CA, United States
² Mathematics Department, Harvard University, Cambridge, MA, United States

Geometry & topology, Tome 27 (2023) no. 5, pp. 1891-1946.

Résumé

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 and the GIT compactification of Miranda.

Détail

DOI : 10.2140/gt.2023.27.1891

Keywords: moduli spaces, elliptic surfaces, K3 surfaces, KSBA, stable pairs, twisted stable maps

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