Focal loci of families
and the genus of curves on surfaces
Authors:
Luca Chiantini and Angelo Felice Lopez
Journal:
Proc. Amer. Math. Soc. 127 (1999), 3451-3459
MSC (1991):
Primary 14J29; Secondary 32H20, 14C20
DOI:
https://doi.org/10.1090/S0002-9939-99-05407-6
Published electronically:
July 23, 1999
Corrigendum:
Proc. Amer. Math. Soc. 137 (2009), 3951-3951.
MathSciNet review:
1676295
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: In this article we apply the classical method of focal loci of families to give a lower bound for the genus of curves lying on general surfaces. First we translate and reprove Xu's result that any curve on a general surface in
of degree
has geometric genus
. Then we prove a similar lower bound for the curves lying on a general surface in a given component of the Noether-Lefschetz locus in
and on a general projectively Cohen-Macaulay surface in
.
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Additional Information
Luca Chiantini
Affiliation:
Dipartimento di Matematica, Università di Siena, Via del Capitano 15, 53100 Siena, Italy
Email:
chiantini@unisi.it
Angelo Felice Lopez
Affiliation:
Dipartimento di Matematica, Università di Roma Tre, Largo San Leonardo Murialdo 1, 00146 Roma, Italy
Email:
lopez@matrm3.mat.uniroma3.it
DOI:
https://doi.org/10.1090/S0002-9939-99-05407-6
Received by editor(s):
February 2, 1998
Published electronically:
July 23, 1999
Additional Notes:
This research was partially supported by the MURST national project “Geometria Algebrica"; the authors are members of GNSAGA of CNR
Communicated by:
Ron Donagi
Article copyright:
© Copyright 1999
American Mathematical Society