Prym varieties and projective structures on Riemann surfaces

Indranil Biswas; Alessandro Ghigi; Luca Vai

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arXiv · 2506.02871

Prym varieties and projective structures on Riemann surfaces

Indranil Biswas·Alessandro Ghigi·Luca Vai

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Abstract

Given an \'etale double covering $\pi\, :\, \widetilde{C}\, \longrightarrow\, C$ of compact Riemannsurfaces with $C$ of genus at least two, we use the Prym variety of the cover to construct canonical projective structures on both $\widetilde C$ and $C$. This construction can be interpreted as a section of an affine bundle over the moduli space of \'etale double covers. The $\overline{\partial}$--derivative of this section is a (1,1)--form on the moduli space. We compute this derivative in terms of Thetanullwert maps. Using the Schottky--Jung identities we show that, in general, the projective structure on $C$ depends on the cover.

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BibTeX RIS

Indranil Biswas, Alessandro Ghigi, Luca Vai. 2025-06-03. Prym varieties and projective structures on Riemann surfaces. https://arxiv.org/abs/2506.02871

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