Relative mirror symmetry, theta functions and the Gamma conjecture
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915437118226432 |
|---|---|
| author | You, Fenglong |
| author_facet | You, Fenglong |
| contents | Let $X$ be a Fano variety, and $D\subset X$ be an snc anticanonical divisor. We study relative mirror symmetry for the log Calabi--Yau pair $(X,D)$. (1) We prove a relative mirror theorem for snc pairs without assuming the divisors are nef. (2) We study theta functions associated with the pair $(X,D)$. (3) We introduce functions on the mirror that are obtained from the higher-degree part of the big relative quantum cohomology. As an application, we use these new ingredients in relative mirror symmetry to prove a version of the mirror symmetric Gamma conjecture for $X$ for $\mathcal O_X$ and $\mathcal O_{\operatorname{pt}}$ in this setting, where the Landau--Ginzburg potential is defined as a sum of theta functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06750 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relative mirror symmetry, theta functions and the Gamma conjecture You, Fenglong Algebraic Geometry Let $X$ be a Fano variety, and $D\subset X$ be an snc anticanonical divisor. We study relative mirror symmetry for the log Calabi--Yau pair $(X,D)$. (1) We prove a relative mirror theorem for snc pairs without assuming the divisors are nef. (2) We study theta functions associated with the pair $(X,D)$. (3) We introduce functions on the mirror that are obtained from the higher-degree part of the big relative quantum cohomology. As an application, we use these new ingredients in relative mirror symmetry to prove a version of the mirror symmetric Gamma conjecture for $X$ for $\mathcal O_X$ and $\mathcal O_{\operatorname{pt}}$ in this setting, where the Landau--Ginzburg potential is defined as a sum of theta functions. |
| title | Relative mirror symmetry, theta functions and the Gamma conjecture |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2508.06750 |