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arXiv · 2407.05539

Moduli of elliptic surfaces of Kodaira dimension one fibered over rational curves

Dori Bejleri·Josiah Foster·Andres Fernandez Herrero·Giovanni Inchiostro·Svetlana Makarova·Junyan Zhao
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Abstract

In this article, we construct an infinite sequence of irreducible components of Koll\'{a}r--Shepherd-Barron (KSB-) moduli spaces of surfaces of arbitrarily large volumes, and describe the boundary of each component completely. Moreover, we describe the stable reduction steps in finding the KSB-limits in an explicit combinatorial way. Our main approach is to study the moduli spaces of elliptic surfaces with Kodaira dimension one, fibered over rational curves, using the techniques of wall-crossing for KSBA moduli and twisted stable maps.

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Dori Bejleri, Josiah Foster, Andres Fernandez Herrero, Giovanni Inchiostro, Svetlana Makarova, Junyan Zhao. 2024-07-08. Moduli of elliptic surfaces of Kodaira dimension one fibered over rational curves. https://arxiv.org/abs/2407.05539

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