Theta functions and adiabatic curvature on an Abelian variety
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866913229882523648 |
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| author | Chang, Ching-Hao Cheng, Jih-Hsin Tsai, I-Hsun |
| author_facet | Chang, Ching-Hao Cheng, Jih-Hsin Tsai, I-Hsun |
| contents | For an ample line bundle $L$ on an Abelian variety $M$, we study the theta functions associated with the family of line bundles $L\otimes T$ on $M$ indexed by $T\in \text{Pic}^{0}(M)$. Combined with an appropriate differential geometric setting, this leads to an explicit curvature computation of the direct image bundle $E$ on $\text{Pic}^{0}(M)$, whose fiber $E_{T}$ is the vector space spanned by the theta functions for the line bundle $L\otimes T$ on $M$. Some algebro-geometric properties of $E$ are also remarked. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_12986 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Theta functions and adiabatic curvature on an Abelian variety Chang, Ching-Hao Cheng, Jih-Hsin Tsai, I-Hsun Algebraic Geometry Differential Geometry 32J25 (Primary) 14K25, 32L10, 14K30, 14F25 (Secondary) For an ample line bundle $L$ on an Abelian variety $M$, we study the theta functions associated with the family of line bundles $L\otimes T$ on $M$ indexed by $T\in \text{Pic}^{0}(M)$. Combined with an appropriate differential geometric setting, this leads to an explicit curvature computation of the direct image bundle $E$ on $\text{Pic}^{0}(M)$, whose fiber $E_{T}$ is the vector space spanned by the theta functions for the line bundle $L\otimes T$ on $M$. Some algebro-geometric properties of $E$ are also remarked. |
| title | Theta functions and adiabatic curvature on an Abelian variety |
| topic | Algebraic Geometry Differential Geometry 32J25 (Primary) 14K25, 32L10, 14K30, 14F25 (Secondary) |
| url | https://arxiv.org/abs/2210.12986 |