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Good moduli spaces for boundary polarized Calabi-Yau surface pairs

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arxiv 2407.00850 v1 pith:76JGZLUI submitted 2024-06-30 math.AG math.DG

Harold Blum , Yuchen Liu This is my paper · ORCID
classification math.AGmath.DG
keywords modulipairsspacesampleboundarycalabi-yaugoodpolarized
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abstract

We construct projective asymptotically good moduli spaces parametrizing boundary polarized CY surface pairs, which are projective slc Calabi-Yau pairs $(X,D)$ such that $D$ is ample and $X$ has dimension two. The moduli space provides a wall crossing between certain KSBA and K-moduli spaces and is the ample model of the Hodge line bundle. In the case of K3 surfaces with a non-symplectic automorphism, the moduli space gives a modular interpretation for the Baily--Borel compactification.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Picard group of the Baily--Borel compactification of the moduli space of quasi-polarized K3 surfaces and generalizations

    math.AG 2024-11 conditional novelty 8.0 of 10

    The Picard group of the Baily-Borel compactification of the moduli space of quasi-polarized K3 surfaces is Z, spanned by the extended Hodge line bundle.

  2. Stable maps to quotient stacks with a properly stable point

    math.AG 2024-11 conditional novelty 7.0 of 10

    A new extended weighted blow-up construction yields proper Deligne-Mumford compactifications of stable maps to quotient stacks with projective good moduli space.

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