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Vector bundle of Prym differentials over Teichmüller spaces of surfaces with punctures. (English) Zbl 07325502

Summary: 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.

MSC:

30F60 Teichmüller theory for Riemann surfaces
30F10 Compact Riemann surfaces and uniformization
30F30 Differentials on Riemann surfaces
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
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References:

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