Inversion of the Abel--Prym map for real curves with involutions
Abstract
Riemann vanishing theorem is a main ingredient of the conventional technique related to the Jacobi inversion problem. In the case of curves with a holomorphic involution, it has been presented quite fully in wellknown Fay's Lectures on theta functions. The case of real algebraic curves with involution is presented with less completeness in the literature. We provide a detailed presentation of that case, including the case of real curves of the non-separating type with a holomorphic involution, not considered before with this relation. In particular, we formulate the symmetry of the Prym theta function in this case.
Keywords
Cite
@article{arxiv.2511.04229,
title = {Inversion of the Abel--Prym map for real curves with involutions},
author = {Oleg K. Sheinman},
journal= {arXiv preprint arXiv:2511.04229},
year = {2026}
}
Comments
13 pages, bibliography 17 items. This version contains minor editorial changes. Lemma 4.1 has been supplemented. Remark 4.2 and Corollary 4.3 have been added. Theorem 4.3 has been corrected and got the mew number 4.5