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arXiv · 2609.03305

Log canonical models of a fixed variety with varying boundaries

Xingying Li·Zhan Li
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Abstract

Motivated by extending the Morrison-Kawamata cone conjecture beyond Calabi-Yau varieties and Severi-Maehara type finiteness results to targets not necessarily of general type, we fix a smooth projective variety and study the finiteness of its log canonical models as klt boundaries vary. Our main result establishes finiteness for every smooth projective minimal surface. For each $κ\in\{-\infty,0,1\}$, we construct a smooth projective non-minimal surface of Kodaira dimension $κ$ with infinitely many log canonical models, showing that the minimality assumption cannot be omitted in general. We also investigate possible extensions of this finiteness result to higher dimensions.

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Xingying Li, Zhan Li. 2026-09-11. Log canonical models of a fixed variety with varying boundaries. https://arxiv.org/abs/2609.03305

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