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Sibirskii Matematicheskii Zhurnal, 2014, Volume 55, Number 2, Pages 379–395
(Mi smj2541)
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This article is cited in 1 scientific paper (total in 1 paper)
The space of harmonic Prym differentials on a variable compact Riemann surface
T. A. Pushkarevaa, V. V. Chueshevb a Gorno-Altaisk State University, Gorno-Altaisk, Russia
b Kemerovo State University, Kemerovo, Russia
Abstract:
The harmonic Prym differentials and their period classes play an important role in the modern theory of functions on compact Riemann surfaces [1–7]. We study the harmonic Prym bundle, whose fibers are the spaces of harmonic Prym differentials on variable compact Riemann surfaces and find its connection with Gunning's cohomological bundle over the Teichmüller space for two important subgroups of the inessential and normalized characters on a compact Riemann surface. We study the periods of holomorphic Prym differentials for essential characters on variable compact Riemann surfaces.
Keywords:
harmonic Prym differential, abelian differential, character, Teichmüller space.
Received: 27.07.2013
Citation:
T. A. Pushkareva, V. V. Chueshev, “The space of harmonic Prym differentials on a variable compact Riemann surface”, Sibirsk. Mat. Zh., 55:2 (2014), 379–395; Siberian Math. J., 55:2 (2014), 309–322
Linking options:
https://www.mathnet.ru/eng/smj2541 https://www.mathnet.ru/eng/smj/v55/i2/p379
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