Periods of harmonic Prym differentials on a compact Riemann surface

V. V. Chueshev

Kemerovo State University

Abstract: We study the period classes of closed, harmonic, and holomorphic Prym differentials on a compact Riemann surface of any genus $g\geq 2$ for arbitrary characters of its fundamental group. We prove that the harmonic Prym vector bundle of harmonic Prym differentials and the Gunning cohomology bundle are real-analytically isomorphic over the base of nontrivial normalized characters for every compact Riemann surface of genus $g\geq 2$.

Keywords: compact Riemann surface, harmonic Prym differential.

UDC: 515.17:517.545

Received: 11.04.2001

 English version: Siberian Mathematical Journal, 2002, 43:4, 756–768

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