The maximal rank conjecture and rank two Brill-Noether theory
Algebraic Geometry
2011-09-13 v2
Abstract
We describe applications of Koszul cohomology to the Brill-Noether theory of rank 2 vector bundles. Among other things, we show that in every genus g>10, there exist curves invalidating Mercat's Conjecture for rank 2 bundles. On the other hand, we prove that Mercat's Conjecture holds for general curves of bounded genus, and its failure locus is a Koszul divisor in the moduli space of curves. We also formulate a conjecture concerning the minimality of Betti diagrams of suitably general curves, and point out its consequences to rank 2 Brill-Noether theory.
Cite
@article{arxiv.1010.4060,
title = {The maximal rank conjecture and rank two Brill-Noether theory},
author = {Gavril Farkas and Angela Ortega},
journal= {arXiv preprint arXiv:1010.4060},
year = {2011}
}
Comments
21 pages. Title slightly changed, various minor corrections. To appear in Pure and Applied Mathematics Quarterly, volume dedicated to Eckart Viehweg