Vector bundle of prym differentials over Teichmüller spaces of surfaces with punctures

Alexander V. Chueshev, Victor V. Chueshev

Institute of Fundamental Sciences, Kemerovo State University, Krasnaya, 6, Kemerovo, 650043, Russia

Abstract: In this paper we study multiplicative meromorphic functions and differentials on Riemann surfaces of finite type. We prove an analog of P. Appell's formula on decomposition of multiplicative functions with poles of arbitrary multiplicity into a sum of elementary Prym integrals. We construct explicit bases for some important quotient spaces and prove a theorem on a fiber isomorphism of vector bundles and $n!$-sheeted mappings over Teichmüller spaces. This theorem gives an important relation between spaces of Prym differentials (Abelian differentials) on a compact Riemann surfaces and on a Riemann surfaces of finite type.

Keywords: Teichmüller spaces for Riemann surfaces of finite type, Prym differentials, vector bundles, group of characters, Jacobi manifolds.

UDC: 515.17+517.545

Received: 12.10.2018
Received in revised form: 18.01.2019
Accepted: 04.03.2019

Language: English

DOI: 10.17516/1997-1397-2019-12-3-263-275

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