On Irregular Holomorphic Mappings between Riemann Surfaces of Genera Four and Two
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 2, pp. 72-79 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the present paper we describe the structure of irregular holomorphic mappings between Riemann surfaces of genera four and two. The regular was considered earlier by Takao Kato. The obtained results are supposed to be used to give a sharp upper bound for the number of all holomorphic mappings between the above surfaces. This bound is still unknown yet.
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I. A. Mednykh. On Irregular Holomorphic Mappings between Riemann Surfaces of Genera Four and Two. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 2, pp. 72-79. http://geodesic.mathdoc.fr/item/VNGU_2009_9_2_a7/

[1] Mednykh I. A., “O golomorfnykh otobrazheniyakh rimanovoi poverkhnosti roda tri na rimanovu poverkhnost roda dva”, Dokl. Akademii nauk, 424:2 (2009), 165–167 | Zbl

[2] Accola R. D. M., “On Lifting the Hyperelliptic Involution”, Proc. Amer. Math. Soc., 122:2 (1994), 341–347 | DOI | MR | Zbl

[3] Alzati A., Pirola G. P., “Some Remarks on the de Franchis Theorem”, Ann. Univ. Ferrara Sez. VII (N.S.), 36 (1990), 45–52 | MR | Zbl

[4] Farkas H. M., Kra I., Riemann Surfaces, Graduate Texts in Mathematics, 71, Springer-Verlag, N. Y.–Berlin, 1980 | DOI | MR | Zbl

[5] Franchis M. de, “Un Teorema Sulle Involuzioni Irrazionali”, Rend. Circ. Mat. Palermo, 36 (1913), 368 | DOI | Zbl

[6] Goldberg L. R., “Catalan Numbers and Branched Coverings by the Riemann Sphere”, Advances in Mathematics, 85 (1991), 129–144 | DOI | MR | Zbl

[7] Howard A., Sommese A. J., “On the Theorem of de Franchis”, Ann. Scoula. Norm. Sup. Pisa Cl. Sci., 4:10 (1983), 429–436 | MR

[8] Hurwitz A., “Über Algebraische Gebilde mit Eindentigen Transformationen in Sich”, Math. Ann., 41 (1893), 403–442 | DOI | MR

[9] Kato T., “On Riemann Surfaces of Genus Four with Non-Trivial Automorphisms”, Kodai Math. J., 1981, no. 4, 443–456 | DOI | MR | Zbl

[10] Macbeath A. M., “On a Theorem of Hurwitz”, Proc. Glasgow Math. Assoc., 1961, no. 5, 90–96 | DOI | MR | Zbl

[11] Martens H., “A Remark on Abel's Theorem and the Mapping of Linear Series”, Comment. Math. Helvetici, 1977, no. 52, 557–559 | DOI | MR | Zbl

[12] Tanabe M., “A Bound for the Theorem of de Franchis”, Proc. Amer. Math. Soc., 127 (1999), 2289–2295 | DOI | MR | Zbl

[13] Tanabe M., “Holomorphic Maps of Riemann Surfaces and Weierstrass Points”, Kodai Math. J., 28:2 (2005), 423–429 | DOI | MR | Zbl

[14] Thurston W. P., The Geometry and Topology of Three-Manifolds, Princeton Univ. Math. Dept., 1978