Double covering of curves
Authors:
Edoardo Ballico, Changho Keem and Seungsuk Park
Journal:
Proc. Amer. Math. Soc. 132 (2004), 3153-3158
MSC (2000):
Primary 14H51, 14H30
DOI:
https://doi.org/10.1090/S0002-9939-04-07426-X
Published electronically:
May 12, 2004
MathSciNet review:
2073288
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Let be a smooth projective algebraic curve of genus
and
an integer with
. For all integers
we prove the existence of a double covering
with
a smooth curve of genus
and the existence of a degree
morphism
that does not factor through
. By the Castelnuovo-Severi inequality, the result is sharp (except perhaps the bound
).
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Additional Information
Edoardo Ballico
Affiliation:
Department of Mathematics, Università di Trento, 38050 Povo(TN), Italy
Email:
ballico@science.unitn.it
Changho Keem
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, South Korea
Email:
ckeem@math.snu.ac.kr
Seungsuk Park
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, South Korea
Address at time of publication:
Mathematics Section, The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy
Email:
s2park@math.snu.ac.kr, spark@ictp.trieste.it
DOI:
https://doi.org/10.1090/S0002-9939-04-07426-X
Keywords:
Double coverings,
base-point-free pencil,
Castelnuovo-Severi inequality,
Brill-Noether theory
Received by editor(s):
January 15, 2001
Received by editor(s) in revised form:
July 7, 2003
Published electronically:
May 12, 2004
Additional Notes:
The first named author was partially supported by MIUR and GNSAGA of INdAM (Italy). The second named author was supported by Korea Research Foundation Grant #2001-015-DS0003.
Communicated by:
Michael Stillman
Article copyright:
© Copyright 2004
American Mathematical Society