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Non-semistable Arakelov bound and hyperelliptic Szpiro ratio for function fields
Author(s):
Khac
Viet
Nguyen
Journal:
Proc. Amer. Math. Soc.
127
(1999),
3125-3130.
MSC (1991):
Primary 11G30, 14H05
Posted:
July 12, 1999
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Abstract:
We prove a complex function field analogue of Szpiro's conjecture for hyperelliptic curves and some applications. The cases of function fields of positive characteristic and number fields are discussed briefly.
References:
- [A]
- Arakelov, S. Yu., Families of algebraic curves with fixed degeneracy, Math. USSR Izv., v.5 (1971), 1277-1302. MR 48:298
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- Nguyen, K. V., On Beauville's conjecture and related topics, J. of Math. of Kyoto Univ., 35-2 (1995), 275-298. MR 96m:14032b
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- Nguyen, K. V., On families of curves over
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Additional Information:
Khac
Viet
Nguyen
Affiliation:
Institute of Mathematics, P.O. Box 631, Bo Ho, 10000, Hanoi, Vietnam
Email:
nkviet@thevinh.ncst.ac.vn
DOI:
10.1090/S0002-9939-99-05426-X
PII:
S 0002-9939(99)05426-X
Keywords:
Non-semistable,
hyperelliptic,
Arakelov bound,
Szpiro ratio
Received by editor(s):
June 12, 1997
Posted:
July 12, 1999
Additional Notes:
The research was partially supported by the National Natural Science Basic Research Foundation of Vietnam.
Dedicated:
Dedicated to the memory of Professor K. Kodaira
Communicated by:
Ron Donagi
Copyright of article:
Copyright
1999,
American Mathematical Society
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