On symmetric products of curves
Author:
F. Bastianelli
Journal:
Trans. Amer. Math. Soc. 364 (2012), 2493-2519
MSC (2010):
Primary 14E05, 14Q10; Secondary 14J29, 14H51, 14N05
DOI:
https://doi.org/10.1090/S0002-9947-2012-05378-5
Published electronically:
January 19, 2012
MathSciNet review:
2888217
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Let be a smooth complex projective curve of genus
and let
be its second symmetric product. This paper concerns the study of some attempts at extending to
the notion of gonality. In particular, we prove that the degree of irrationality of
is at least
when
is generic and that the minimum gonality of curves through the generic point of
equals the gonality of
. In order to produce the main results we deal with correspondences on the
-fold symmetric product of
, with some interesting linear subspaces of
enjoying a condition of Cayley-Bacharach type, and with monodromy of rational maps. As an application, we also give new bounds on the ample cone of
when
is a generic curve of genus
.
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Additional Information
F. Bastianelli
Affiliation:
Dipartimento di Matematica, Università degli Studi di Pavia, via Ferrata 1, 27100 Pavia, Italy
Address at time of publication:
Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, via Cozzi 53, 20125 Milano, Italy
Email:
francesco.bastianelli@unipv.it, francesco.bastianelli@unimib.it
DOI:
https://doi.org/10.1090/S0002-9947-2012-05378-5
Received by editor(s):
February 2, 2010
Received by editor(s) in revised form:
April 30, 2010
Published electronically:
January 19, 2012
Additional Notes:
This work was partially supported by PRIN 2007 “Spazi di moduli e teorie di Lie”, INdAM (GNSAGA), and FAR 2008 (PV) “Varietà algebriche, calcolo algebrico, grafi orientati e topologici”.
Article copyright:
© Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.