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A bound for the theorem of de Franchis
Author(s):
Masaharu
Tanabe
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2289-2295.
MSC (1991):
Primary 30F30
Posted:
April 9, 1999
MathSciNet review:
1600153
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Abstract:
We give a bound on the number of nonconstant holomorphic maps between compact Riemann surfaces of genera  .
References:
- [F-K]
- Farkas, H.M., Kra, I., Riemann surfaces, Springer-Verlag, New York, Heidelberg, and Berlin, 1980. MR 82c:30067
- [F]
- de Franchis, M., Un teorema sulle involuzioni irrazionali, Rend. Circ. Mat. Palermo 36 (1913), 368.
- [H-S]
- Howard, A., Sommese, A. J., On the theorem of de Franchis, Ann. Scoula. Norm. Sup. Pisa Cl. Sci. (4) 10 (1983), 429-436. MR 85k:32048
- [H]
- Hurwitz, A., Über algebraischen Gebilde mit eindeutigen Transformation in sich, Math. Ann. 41 (1893), 403-442.
- [I1]
- Imayoshi, Y., An analytic proof of Severi's theorem, Complex Variables Theory Appl. 2 (1983), 151-155. MR 85j:32037
- [I2]
- -, Generalizations of de Franchis theorem, Duke Math. J. 50 (1983), 393-408. MR 85d:32051
- [K]
- Kani, E., Bounds on the number of non-rational subfields of a function field, Invent. Math. 85 (1986), 185-198. MR 87i:14021
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- Macbeath, A. M., On a theorem of Hurwitz, Proc. Glasgow Math. Assoc. 5 (1961), 90-96.
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- Martens, H., A new proof of Torelli's theorem, Ann. of Math. (2) 78 (1963), 107-111. MR 27:2506
- [Mr2]
- -, Observations on morphisms of closed Riemann surfaces, Bull. London Math. Soc. 10 (1978), 209-212. MR 58:1132
- [Mr3]
- -, Mappings of closed Riemann surfaces, Proc. Sympos. Pure Math. 49, Part 1 (1989), 531-539. MR 90i:14030
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- [W]
- Weyl, H., On generalized Riemann matrices, Ann. of Math. (2) 35 (1934), 714-729.
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Additional Information:
Masaharu
Tanabe
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, Ohokayama, Meguro, Tokyo, 152-8551, Japan
Email:
tanabe@math.titech.ac.jp
DOI:
10.1090/S0002-9939-99-04858-3
PII:
S 0002-9939(99)04858-3
Received by editor(s):
August 19, 1997
Received by editor(s) in revised form:
October 27, 1997
Posted:
April 9, 1999
Communicated by:
Albert Baernstein II
Copyright of article:
Copyright
1999,
American Mathematical Society
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