Moduli of surfaces fibered in (log) Calabi-Yau pairs II: elliptic surfaces

Giovanni Inchiostro; Junyan Zhao

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arXiv · 2512.24017

Moduli of surfaces fibered in (log) Calabi-Yau pairs II: elliptic surfaces

Giovanni Inchiostro·Junyan Zhao

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Abstract

This paper continues the study initiated in [ISZ25] on the moduli of surfaces admitting lc-trivial fibrations. Using the techniques developed in [ISZ25], we (1) provide a classification of the surfaces appearing on the boundary of the KSBA-moduli space of elliptic surfaces with a bisection (2) recover the results of a series of papers on the moduli stacks of elliptic surfaces with a section [AB22, Inc20, Bru15]. Notably, our proof of (2) avoids the use of explicit steps of an MMP, such as the "La Nave flip" from [LN02], which plays a central role in [AB22,Inc20]. As an application, we compactify the moduli stack of hyperelliptic K3 surfaces.

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BibTeX RIS

Giovanni Inchiostro, Junyan Zhao. 2025-12-30. Moduli of surfaces fibered in (log) Calabi-Yau pairs II: elliptic surfaces. https://arxiv.org/abs/2512.24017

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