2003/10/18 by Pablo Ares-Gastesi, Indranil Biswas
Mathematics · #math.AG #math.CV
published as Proc. Indian Acad. Sci. (Math. Sci.), Vol. 113, No. 2, May 2003, pp. 139-152 · 13 pages
arxiv created 2003/10/18 · arxiv updated 2009/12/01
Using divisors, an analog of the Jacobian for a compact connected nonorientable Klein surface Y is constructed. The Jacobian is identified with the dual of the space of all harmonic real one-forms on Y quotiented by the torsion-free part of the first integral homology of Y. Denote by X the double cover of Y given by orientation. The Jacobian of Y is identified with the space of all degree zero holomorphic line bundles L over X with the property that L is isomorphic to σ^*L, where σ is the involution of X.