Geography of Landau-Ginzburg models and threefold syzygies
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918080668499968 |
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| author | He, Yang Sheshmani, Artan |
| author_facet | He, Yang Sheshmani, Artan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15427 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geography of Landau-Ginzburg models and threefold syzygies He, Yang Sheshmani, Artan Algebraic Geometry 14E05, 14E07, 14E30 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. |
| title | Geography of Landau-Ginzburg models and threefold syzygies |
| topic | Algebraic Geometry 14E05, 14E07, 14E30 |
| url | https://arxiv.org/abs/2506.15427 |