Syzygies of curves and the effective cone of \bar{M}_g
| dc.creator | Farkas, Gavril | |
| dc.date | 2005-03-23 | |
| dc.date | 2006-12-07 | |
| dc.date.accessioned | 2026-07-07T06:39:39Z | |
| dc.date.available | 2026-07-07T06:39:39Z | |
| dc.description | We describe a systematic way of constructing effective divisors on the moduli space of stable curves of genus g having exceptionally small slope. We prove that any divisor on \bar{M}_g consisting of curves failing a certain Green-Lazarsfeld syzygy type condition, provides a counterexample to the Harris-Morrison Slope Conjecture. These divisors generalize our original isolated counterexample to the Slope Conjecture which was the divisor on M_{10} of curves lying on K3 surfaces. We also introduce a new stratification of M_g, somewhat similar to the classical stratification given by gonality, but where the analogue of hyperelliptic curves are sections of K3 surfaces. Finally, we prove that various moduli spaces M_{g,n} with g<23 are of general type. | |
| dc.description | 34 pages; Typos corrected. Version published in Duke Math. J | |
| dc.identifier | https://arxiv.org/abs/math/0503498 | |
| dc.identifier | http://arxiv.org/abs/math/0503498 | |
| dc.identifier | Duke Math. J. 135 (2006), 53-99. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101154 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H10 | |
| dc.title | Syzygies of curves and the effective cone of \bar{M}_g | |
| dc.type | text |