Normal Functions, Even Theta Characteristics and the Theta Divisor
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917431220371456 |
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| author | Biswas, Indranil Fassina, Lorenzo Pirola, Gian Pietro |
| author_facet | Biswas, Indranil Fassina, Lorenzo Pirola, Gian Pietro |
| contents | Let $[C]$ be a general point in the moduli space of curves $M_g$ with $g > 1$. Let $G \subset J(C)$ be a connected compact subgroup of real dimension $1$ of the Jacobian, and let $L$ be an even theta characteristic on $C$. We prove that $\{ζ\in G \mid H^0(C, L \otimes ζ) \neq 0\} = \emptyset$ if and only if $L \otimes ζ_G$ is an even theta characteristic on $C$, where $ζ_G$ is the unique non-trivial point of $G$ of order two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21661 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Normal Functions, Even Theta Characteristics and the Theta Divisor Biswas, Indranil Fassina, Lorenzo Pirola, Gian Pietro Algebraic Geometry Let $[C]$ be a general point in the moduli space of curves $M_g$ with $g > 1$. Let $G \subset J(C)$ be a connected compact subgroup of real dimension $1$ of the Jacobian, and let $L$ be an even theta characteristic on $C$. We prove that $\{ζ\in G \mid H^0(C, L \otimes ζ) \neq 0\} = \emptyset$ if and only if $L \otimes ζ_G$ is an even theta characteristic on $C$, where $ζ_G$ is the unique non-trivial point of $G$ of order two. |
| title | Normal Functions, Even Theta Characteristics and the Theta Divisor |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2604.21661 |