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arXiv · 2506.15427

Geography of Landau-Ginzburg models and threefold syzygies

Yang He·Artan Sheshmani
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Abstract

We study the behavior of toric Landau-Ginzburg models under extremal contraction and minimal model program. We also establish a relation between the moduli space of toric Landau-Ginzburg models and the geography of central models. We conjecture that there is a correspondence between extremal contractions and minimal model program on Fano varieties, and degenerations of their associated toric Landau-Ginzburg models written explicitly. We prove the conjectures for smooth toric varieties, as well as general smooth Fano varieties in dimensions 2 and 3. As an application, we compute the elementary syzygies for smooth Fano threefolds.

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Yang He, Artan Sheshmani. 2025-06-18. Geography of Landau-Ginzburg models and threefold syzygies. https://arxiv.org/abs/2506.15427

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