• The Jacobian of a nonorientable Klein surface

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/113/02/0139-0152

• # Keywords

Nonorientable surface; divisor; Jacobian

• # Abstract

Using divisors, an analog of the Jacobian for a compact connected nonorientable Klein surfaceY is constructed. The Jacobian is identified with the dual of the space of all harmonic real one-forms onY quotiented by the torsion-free part of the first integral homology ofY. Denote byX the double cover ofY given by orientation. The Jacobian ofY is identified with the space of all degree zero holomorphic line bundlesL overX with the property thatL is isomorphic to σ*/-L, where σ is the involution ofX.

• # Author Affiliations

1. School of Mathematics, Tata Institute of Fundamental Research, Mumbai - 400 005, India

• # Proceedings – Mathematical Sciences

Volume 132, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019