A bound for the theorem of de Franchis
HTML articles powered by AMS MathViewer
- by Masaharu Tanabe PDF
- Proc. Amer. Math. Soc. 127 (1999), 2289-2295 Request permission
Abstract:
We give a bound on the number of nonconstant holomorphic maps between compact Riemann surfaces of genera $>1$.References
- Hershel M. Farkas and Irwin Kra, Riemann surfaces, Graduate Texts in Mathematics, vol. 71, Springer-Verlag, New York-Berlin, 1980. MR 583745
- de Franchis, M., Un teorema sulle involuzioni irrazionali, Rend. Circ. Mat. Palermo 36 (1913), 368.
- Alan Howard and Andrew J. Sommese, On the theorem of de Franchis, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 10 (1983), no. 3, 429–436. MR 739918
- Hurwitz, A., Über algebraischen Gebilde mit eindeutigen Transformation in sich, Math. Ann. 41 (1893), 403-442.
- Yôichi Imayoshi, An analytic proof of Severi’s theorem, Complex Variables Theory Appl. 2 (1983), no. 2, 151–155. MR 725265, DOI 10.1080/17476938308814038
- Yôichi Imayoshi, Generalizations of de Franchis theorem, Duke Math. J. 50 (1983), no. 2, 393–408. MR 705032, DOI 10.1215/S0012-7094-83-05017-2
- Ernst Kani, Bounds on the number of nonrational subfields of a function field, Invent. Math. 85 (1986), no. 1, 185–198. MR 842053, DOI 10.1007/BF01388797
- Macbeath, A. M., On a theorem of Hurwitz, Proc. Glasgow Math. Assoc. 5 (1961), 90-96.
- Henrik H. Martens, A new proof of Torelli’s theorem, Ann. of Math. (2) 78 (1963), 107–111. MR 152528, DOI 10.2307/1970505
- Henrik H. Martens, Observations on morphisms of closed Riemann surfaces, Bull. London Math. Soc. 10 (1978), no. 2, 209–212. MR 480985, DOI 10.1112/blms/10.2.209
- Henrik H. Martens, Mappings of closed Riemann surfaces, Theta functions—Bowdoin 1987, Part 1 (Brunswick, ME, 1987) Proc. Sympos. Pure Math., vol. 49, Amer. Math. Soc., Providence, RI, 1989, pp. 531–539. MR 1013150, DOI 10.1002/cpa.3160160202
- Masaharu Tanabe, On rigidity of holomorphic maps of Riemann surfaces, Osaka J. Math. 33 (1996), no. 2, 485–496. MR 1416060
- Weyl, H., On generalized Riemann matrices, Ann. of Math. (2) 35 (1934), 714-729.
Additional Information
- Masaharu Tanabe
- Affiliation: Department of Mathematics, Tokyo Institute of Technology, Ohokayama, Meguro, Tokyo, 152-8551, Japan
- Email: tanabe@math.titech.ac.jp
- Received by editor(s): August 19, 1997
- Received by editor(s) in revised form: October 27, 1997
- Published electronically: April 9, 1999
- Communicated by: Albert Baernstein II
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2289-2295
- MSC (1991): Primary 30F30
- DOI: https://doi.org/10.1090/S0002-9939-99-04858-3
- MathSciNet review: 1600153