JournalsprimsVol. 27 , No. 3DOI 10.2977/prims/1195169663

A Generalization of Eichler Integrals and Certain Local Systems over Spin Riemann Surfaces

  • Kyoji Saito

    Kyoto University, Japan
A Generalization of Eichler Integrals and Certain Local Systems over Spin Riemann Surfaces cover

Abstract

Let (X, _KX_1/2) be a spin Riemann surface*) of genus ≥ 2. By using infinite dimensional representations of the fundamental group of X, we obtain many local systems on X, which taken together define a resolution of the halfcanonical ring of X and indicate a non-abelian theory of abelian integrals on X. The work has a root in a study of the complex structure on the Fricke moduli space [14]. *) a Riemann surface together with a halfcanonical bundle (4.1).