|
Bounds on the number of holomorphic maps of compact Riemann surfaces
Author(s):
Masaharu
Tanabe
Journal:
Proc. Amer. Math. Soc.
133
(2005),
3057-3064.
MSC (2000):
Primary 30F30
Posted:
April 19, 2005
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We give bounds on the number of nonconstant holomorphic maps of compact Riemann surfaces of genera  .
References:
-
- [A-P]
- Alzati, A., Pirola, G.P., Some remarks on the de Franchis theorem, Ann. Univ. Ferrara Sez. VII (N.S.) 36 (1990), 45-52. MR 1151481 (93b:14041)
- [C]
- Cassels, J.W.S., An Introduction to the geometry of numbers, 2nd pr., Springer-Verlag, New York, Heidelberg, and Berlin, 1971.MR 0306130 (46:5257)
- [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 0739918 (85k:32048)
- [K]
- Kani, E., Bounds on the number of non-rational subfields of a function field, Invent. Math. 85 (1986), 185-198. MR 0842053 (87i:14021)
- [L]
- Lang, S., Abelian varieties, Springer-Verlag, New York, Heidelberg, and Berlin, 1983.MR 0713430 (84g:14041)
- [L-B]
- Lange, H., Birkenhake, Ch., Complex abelian varieties, Springer-Verlag, New York, Heidelberg, and Berlin, 1992.MR 1217487 (94j:14001)
- [Mr1]
- Martens, H., Observations on morphisms of closed Riemann surfaces, Bull. London Math. Soc. 10 (1978), 209-212. MR 0480985 (58:1132)
- [Mr2]
- -, Mappings of closed Riemann surfaces, Proc. Sympos. Pure Math. 49, Part 1 (1989), 531-539. MR 1013150 (90i:14030)
- [Mm]
- Mumford, D., Abelian varieties, Oxford University Press, London, 1970. MR 0282985 (44:219)
- [T1]
- Tanabe, M., On rigidity of holomorphic maps of Riemann surfaces, Osaka J. Math. 33 (1996), 485-496. MR 1416060 (97i:32024)
- [T2]
- -, A bound for the theorem of de Franchis, Proc. Amer. Math. Soc. 127 (1999), 2289-2295. MR 1600153 (99j:30046)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
30F30
Retrieve articles in all Journals with MSC
(2000):
30F30
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/S0002-9939-05-07882-2
PII:
S 0002-9939(05)07882-2
Received by editor(s):
March 26, 2002
Received by editor(s) in revised form:
June 2, 2004
Posted:
April 19, 2005
Additional Notes:
The author's research was partially supported by the Japan-U.S. Cooperative Science Program
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org