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Compactifications of
moduli of elliptic K3 surfaces: Stable pair and toroidal
Valery Alexeev, Adrian Brunyate and Philip Engel |
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Geometry & Topology 26 (2022) 3525–3588
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DOI: 10.2140/gt.2022.26.3525
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Abstract |
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We describe two geometrically meaningful compactifications of the moduli space of elliptic K3 surfaces via stable slc pairs, for two different choices of a polarizing divisor, and show that their normalizations are two different toroidal compactifications of the moduli space, one for the ramification divisor and another for the rational curve divisor. In the course of the proof, we further develop the theory of integral–affine spheres with 24 singularities. We also construct moduli of rational (generalized) elliptic stable slc surfaces of types , and . |
Keywords
K3 surfaces, elliptic surfaces, moduli, KSBA
compactification, stable pairs
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Mathematical Subject Classification
Primary: 14J10
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References |
Publication
Received: 30 October 2020
Revised: 8 August 2021
Accepted: 6 September 2021
Published: 16 March 2023
Proposed: Dan Abramovich
Seconded: Gang Tian, Anna Wienhard
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Authors |
| Valery Alexeev | |
| Department of Mathematics University of Georgia Athens, GA United States |
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| Adrian Brunyate | |
| Baltimore, MD United States |
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| Philip Engel | |
| Department of Mathematics University of Georgia Athens, GA United States |
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