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arXiv · 2401.16037

Theta functions and projective structures

Indranil Biswas·Alessandro Ghigi·Luca Vai
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Abstract

Given a compact Riemann surface $X$, we consider the line, in the space of sections of $2\Theta$ on $J^0(X)$, orthogonal to all the sections that vanish at the origin. This line produces a natural meromorphic bidifferential on $X\times X$ with a pole of order two on the diagonal. This bidifferential is extensively investigated. In particular we show that it produces a projective structure on $X$ which is different from the standard ones.

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Indranil Biswas, Alessandro Ghigi, Luca Vai. 2024-01-29. Theta functions and projective structures. https://arxiv.org/abs/2401.16037

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