Effective divisors on \bar{M}_g, curves on K3 surfaces and the Slope Conjecture
| dc.creator | Farkas, Gavril | |
| dc.creator | Popa, Mihnea | |
| dc.date | 2003-05-07 | |
| dc.date | 2004-08-31 | |
| dc.date.accessioned | 2026-07-07T04:57:50Z | |
| dc.date.available | 2026-07-07T04:57:50Z | |
| dc.description | We carry out a detailed intersection theoretic analysis of the Deligne-Mumford compactification of the divisor on M_{10} consisting of curves sitting on K3 surfaces. This divisor is not of classical Brill-Noether type, and is known to give a counterexample to the Slope Conjecture. The computation relies on the fact that this divisor has four different incarnations as a geometric subvariety of the moduli space of curves, one of them as a higher rank Brill-Noether divisor consisting of curves with an exceptional rank 2 vector bundle. As an application we describe the birational nature of the moduli space of n-pointed curves of genus 10, for all n. We also show that on M_{11} there are effective divisors of minimal slope and having large Iitaka dimension. This seems to contradict the belief that on M_g the classical Brill-Noether divisors are essentially the only ones of slope 6+12/(g+1). | |
| dc.description | This version combines our earlier preprints "Effective divisors on M_g and a counterexample to the Slope Conjecture" and "The geometry of the divisor of K3 sections" into a single paper. To appear in the Journal of Algebraic Geometry | |
| dc.identifier | https://arxiv.org/abs/math/0305112 | |
| dc.identifier | http://arxiv.org/abs/math/0305112 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67402 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H10 | |
| dc.title | Effective divisors on \bar{M}_g, curves on K3 surfaces and the Slope Conjecture | |
| dc.type | text |