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The Prym vector bundle and Gunning vector bundle over the Teichmüller space. (Russian, English) Zbl 1006.14010

Sib. Mat. Zh. 42, No. 4, 937-951 (2001); translation in Sib. Math. J. 42, No. 4, 789-800 (2001).
The author considers Prym differentials, on Riemann surfaces, corresponding to arbitrary characters and gives a construction of the holomorphic Prym vector bundle which parameterizes all holomorphic Prym differentials on Riemann surfaces with fixed genus and arbitrary conformal class for all essential characters, the holomorphic cohomological Gunning vector bundle and the period mapping from the Prym bundle to the Gunning bundle which corresponds to a differential of its periods. He gives a construction of a basis of holomorphic Prym differentials which holomorphically depends on moduli of Riemann surfaces and essential characters.

MSC:

14H60 Vector bundles on curves and their moduli
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
30F30 Differentials on Riemann surfaces
30F60 Teichmüller theory for Riemann surfaces
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