Toric Landau-Ginzburg models in threefold divisorial contractions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866916028735291392 |
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| author | He, Yang Sheshmani, Artan |
| author_facet | He, Yang Sheshmani, Artan |
| contents | We investigate quantum periods and toric Landau-Ginzburg models under divisorial contractions of terminal Fano threefolds. Let $g:Y \rightarrow X$ be a divisorial contraction between $\mathbb{Q}$-factorial Fano threefolds with ordinary terminal singularities and $E$ be the exceptional divisor. Assuming that the center of the contraction is either a smooth point, a terminal quotient point, a point of type cA/n, or a smooth curve with singularities of type cA or cA/n, we prove the regularized period identity
$$
\lim_{r\to+\infty}\hat{G}_{Y,rE}(t)=\hat{G}_X(t)
$$
where $\hat{G}_{Y,rE}(t)$ and $\hat{G}_X(t)$ are the regularized quantum periods of $(Y,rE)$ and $X$ respectively. This gives a mirror approach to the computation of the Sarkisov links and higher syzygies of central models of dimension 3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20126 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Toric Landau-Ginzburg models in threefold divisorial contractions He, Yang Sheshmani, Artan Algebraic Geometry 14E05, 14E07, 14E30 We investigate quantum periods and toric Landau-Ginzburg models under divisorial contractions of terminal Fano threefolds. Let $g:Y \rightarrow X$ be a divisorial contraction between $\mathbb{Q}$-factorial Fano threefolds with ordinary terminal singularities and $E$ be the exceptional divisor. Assuming that the center of the contraction is either a smooth point, a terminal quotient point, a point of type cA/n, or a smooth curve with singularities of type cA or cA/n, we prove the regularized period identity $$ \lim_{r\to+\infty}\hat{G}_{Y,rE}(t)=\hat{G}_X(t) $$ where $\hat{G}_{Y,rE}(t)$ and $\hat{G}_X(t)$ are the regularized quantum periods of $(Y,rE)$ and $X$ respectively. This gives a mirror approach to the computation of the Sarkisov links and higher syzygies of central models of dimension 3. |
| title | Toric Landau-Ginzburg models in threefold divisorial contractions |
| topic | Algebraic Geometry 14E05, 14E07, 14E30 |
| url | https://arxiv.org/abs/2605.20126 |