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Compact moduli of elliptic K3 surfaces

Kenneth Ascher and Dori Bejleri

Geometry & Topology 27 (2023) 1891–1946
Abstract

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.

Keywords
moduli spaces, elliptic surfaces, K3 surfaces, KSBA, stable pairs, twisted stable maps
Mathematical Subject Classification
Primary: 14J10, 14J27, 14J28
Secondary: 14D20
References
Publication
Received: 8 October 2020
Revised: 11 November 2021
Accepted: 17 December 2021
Published: 27 July 2023
Proposed: Mark Gross
Seconded: Jim Bryan, Simon Donaldson
Authors
Kenneth Ascher
Department of Mathematics
University of California, Irvine
Irvine, CA
United States
Dori Bejleri
Mathematics Department
Harvard University
Cambridge, MA
United States

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