Linear series over real and -adic fields

Author:
Brian Osserman

Journal:
Proc. Amer. Math. Soc. **134** (2006), 989-993

MSC (2000):
Primary 14H51, 14P99

Published electronically:
September 28, 2005

MathSciNet review:
2196029

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Abstract | References | Similar Articles | Additional Information

Abstract: We note that the degeneration arguments given by the author in 2003 to derive a formula for the number of maps from a general curve of genus to with prescribed ramification also yields weaker results when working over the real numbers or -adic fields. Specifically, let be such a field: we see that given , , , and satisfying , there exists smooth curves of genus together with points such that all maps from to can, up to automorphism of the image, be defined over . We also note that the analagous result will follow from maps to higher-dimensional projective spaces if it is proven in the case , , and that thanks to work of Sottile, unconditional results may be obtained for special ramification conditions.

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Additional Information

**Brian Osserman**

Affiliation:
Department of Mathematics, University of California Berkeley, Berkeley, California 94720-3840

DOI:
https://doi.org/10.1090/S0002-9939-05-08247-X

Received by editor(s):
March 20, 2004

Received by editor(s) in revised form:
November 7, 2004

Published electronically:
September 28, 2005

Communicated by:
Michael Stillman

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.