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arXiv · 2604.21661

Normal Functions, Even Theta Characteristics and the Theta Divisor

Indranil Biswas·Lorenzo Fassina·Gian Pietro Pirola
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Abstract

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 $\{\zeta \in G \mid H^0(C, L \otimes \zeta) \neq 0\} = \emptyset$ if and only if $L \otimes \zeta_G$ is an even theta characteristic on $C$, where $\zeta_G$ is the unique non-trivial point of $G$ of order two.

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Indranil Biswas, Lorenzo Fassina, Gian Pietro Pirola. 2026-04-23. Normal Functions, Even Theta Characteristics and the Theta Divisor. https://arxiv.org/abs/2604.21661

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