Geodesic
The spaces of meromorphic Prym differentials on finite tori
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 2, pp. 162-172.

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In this article we construct all kinds of elementary Prym differentials for arbitrary characters on a variable torus with a finite numbers of punctures and find the dimensions of two important quotient spaces. As a consequence, this yields the dimension of the first holomorphic de Rham cohomology group of Prym differentials for arbitrary characters on torus. Also, we construct explicit bases in these quotient spaces.
Keywords: Prym differentials for arbitrary characters, the Gunning cohomological bundle over the Teichmuller space torus with a finite numbers of punctures. 
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Olga A. Chuesheva. The spaces of meromorphic Prym differentials on finite tori. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 2, pp. 162-172. http://geodesic.mathdoc.fr/item/JSFU_2014_7_2_a2/

[1] R. C. Gunning, “On the period classes of Prym differentials”, J. Reine Angew. Math., 319 (1980), 153–171 | MR | Zbl

[2] V. V. Chueshev, Multiplicative functions and Prym differentials on a variable compact Riemann surface, Part 2, Kemerov. Gosudarstven. Universitet, Kemerovo, 2003 (in Russian) | Zbl

[3] V. V. Chueshev, “Multiplicative Weierstrass points and Jacobi manifold on a compact Riemann surface”, Mathematical Notes, 74:4 (2003), 629–636 | MR | Zbl

[4] R. Dick, “Holomorphic differentials on punctured Riemann surface”, Differ. Geom. Math. Theor. Phys., Proc. 18 Int. Conf. (Davis, Calif., 2–8 June, 1988), NATO Adv. Sci. Inst. Ser. B Phys., 245, N.-Y.–London, 1990, 475–483 | MR | Zbl

[5] H. M. Farkas, I. Kra, Riemann surfaces, Springer-Verlag, New-York, 1992 | MR | Zbl

[6] L. V. Ahlfors, L. Bers, Spaces of Riemann surfaces and quasi-conformal mappings, Moscow, 1961 (in Russian) | MR

[7] C. J. Earle, “Families of Riemann surfaces and Jacobi varieties”, Annals of Mathematics, 107 (1978), 255–286 | DOI | MR | Zbl

[8] T. S. Krepizina, V. V. Chueshev, “Multiplicative functions and Prym differentials on a variable torus”, Vestnik Novosibirskogo Gosuniversiteta, 12:1 (2012), 74–90 (in Russian)