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arXiv · 2509.07467

Compact moduli of elliptic surfaces with a multiple fiber

Donggun Lee·Yongnam Lee
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Abstract

Motivated by Miranda and Ascher--Bejleri's works on compactifications of the moduli space of rational elliptic surfaces with a section, we study constructions and boundaries of compact moduli spaces of elliptic surfaces with a multiple fiber. Particular emphasis is placed on rational elliptic surfaces without a section and on Dolgachev surfaces. Our main goal is to understand the limit surfaces when a multiple fiber degenerates into an additive type singular fiber, via $\mathbb{Q}$-Gorenstein smoothings of slc surfaces.

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Donggun Lee, Yongnam Lee. 2025-09-09. Compact moduli of elliptic surfaces with a multiple fiber. https://arxiv.org/abs/2509.07467

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