Geodesic
Prym differentials and Teichm\"uller spaces
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 6, pp. 686-691.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this article we study multiplicative meromorphic functions and differentials on Riemann surfaces of finite type. We proved an analogue 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 factor 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 on a compact Riemann surfaces and on a Riemann surfaces of finite type.
Keywords: Teichmüller spaces for Riemann surfaces of finite type, Prym differentials, vector bundles, group of characters, Jacobi manifolds. 
@article{JSFU_2018_11_6_a3,
     author = {Alexander V. Chueshev and Victor V. Chueshev},
     title = {Prym differentials and {Teichm\"uller} spaces},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {686--691},
     publisher = {mathdoc},
     volume = {11},
     number = {6},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2018_11_6_a3/}
}
TY  - JOUR
AU  - Alexander V. Chueshev
AU  - Victor V. Chueshev
TI  - Prym differentials and Teichm\"uller spaces
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2018
SP  - 686
EP  - 691
VL  - 11
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2018_11_6_a3/
LA  - en
ID  - JSFU_2018_11_6_a3
ER  - 
%0 Journal Article
%A Alexander V. Chueshev
%A Victor V. Chueshev
%T Prym differentials and Teichm\"uller spaces
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2018
%P 686-691
%V 11
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2018_11_6_a3/
%G en
%F JSFU_2018_11_6_a3
Alexander V. Chueshev; Victor V. Chueshev. Prym differentials and Teichm\"uller spaces. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 6, pp. 686-691. http://geodesic.mathdoc.fr/item/JSFU_2018_11_6_a3/

[1] A.B. Bogatyrev, “Real meromorphic differentials: a language for describing meron configurations in planar magnetic nanoelements”, Theoretical and Mathematical Physics, 193:1 (2017), 1547–1559 | DOI | MR | Zbl

[2] H.M. Farkas, I. Kra, Riemann surfaces, Grad. Text's Math., 71, Springer, New-York, 1992 | DOI | MR | Zbl

[3] L. Ahlfors, L. Bers, The spaces of Riemann surfaces and quasi-conformal mappings, IL, 1961 (in Russian) | MR

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

[5] V.V. Chueshev, Multiplicative functions and Prym differentials on a variable compact Riemann surface, v. 2, KemGU, Kemerovo, 2003 (in Russian) | Zbl

[6] V.V. Chueshev, M.I. Tulina, “Prym differentials on a variable compact Riemann surface”, Math. Notes, 95:3–4 (2014), 418–433 | MR | Zbl