Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Rational maps between moduli spaces of curves and Gieseker-Petri divisors

Author: Gavril Farkas
Journal: J. Algebraic Geom. 19 (2010), 243-284
Published electronically: June 2, 2009
MathSciNet review: 2580676
Full-text PDF

Abstract | References | Additional Information

Abstract: We study contractions of the moduli space of stable curves beyond the minimal model of $ \overline{\mathcal{M}}_{g'}$ by giving a complete enumerative description of the rational map between two moduli spaces of curves $ \overline{\mathcal{M}}_g \dashrightarrow\overline{\mathcal{M}}_{g'}$ which associates to a curve $ C$ of genus $ g$ its Brill-Noether locus of special divisors in the case this locus is a curve. As an application we construct many examples of moving effective divisors on $ \overline{\mathcal{M}}_g$ of small slope, which in turn can be used to show that various moduli space of curves with level structure are of general type. For low $ g'$ our calculation can be used to study the intersection theory of the moduli space of Prym varieties of dimension $ 5$.

References [Enhancements On Off] (What's this?)

Additional Information

Gavril Farkas
Affiliation: Humboldt-Universität zu Berlin, Institut für Mathematik, 10099 Berlin, Germany

Received by editor(s): September 19, 2007
Received by editor(s) in revised form: December 19, 2007
Published electronically: June 2, 2009
Additional Notes: Research was partially supported by an Alfred P. Sloan Fellowship, the NSF Grants DMS-0450670 and DMS-0500747 and a 2006 Texas Summer Research Assignment. Most of this paper was written while visiting the Institut Mittag-Leffler in Djursholm in the Spring of 2007. Support from the institute is gratefully acknowledged.

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2017 University Press, Inc.
AMS Website