Duke Mathematical Journal

Syzygies of curves and the effective cone of M̲g

Gavril Farkas

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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 M̲g 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

Article information

Source
Duke Math. J., Volume 135, Number 1 (2006), 53-98.

Dates
First available in Project Euclid: 26 September 2006

Permanent link to this document
https://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

Subjects
Primary: 14H10: Families, moduli (algebraic)
Secondary: 13D02: Syzygies, resolutions, complexes

Citation

Farkas, Gavril. Syzygies of curves and the effective cone of $\overline{\mathcal{M}}_g$. Duke Math. J. 135 (2006), no. 1, 53--98. doi:10.1215/S0012-7094-06-13512-3. https://projecteuclid.org/euclid.dmj/1159281064


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