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 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 surfaces
Citation
Gavril Farkas. "Syzygies of curves and the effective cone of ." Duke Math. J. 135 (1) 53 - 98, 1 October 2006. https://doi.org/10.1215/S0012-7094-06-13512-3
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