Syzygies of curves and the effective cone of $\overline{\mathcal{M}}_g$
Gavril Farkas
Source: Duke Math. J. Volume 135, Number 1
(2006), 53-98.
Abstract
We describe a systematic way of constructing effective divisors on the moduli space of stable curves having exceptionally small slope. We show that every codimension 1 locus in $\overline{\mathcal{M}}_g$ consisting of curves failing to satisfy a Green-Lazarsfeld syzygy-type condition provides a counterexample to the Harris-Morrison slope conjecture. We also introduce a new geometric stratification of the moduli space of curves somewhat similar to the classical stratification given by gonality but where the analogues of hyperelliptic curves are the sections of $K3$ surfaces
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1159281064
Digital Object Identifier: doi:10.1215/S0012-7094-06-13512-3
Mathematical Reviews number (MathSciNet): MR2259923
Zentralblatt MATH identifier: 1107.14019
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