The maximal rank conjecture and rank two Brill-Noether theory

Details The maximal rank conjecture and rank two Brill-Noether theory The maximal rank conjecture and rank two Brill-Noether theory

2010-10-19

arxiv.org/abs/1010.4060v2

Pure and Applied Mathematics Quarterly 7 (2011), 1265-1296

Mathematics

Algebraic Geometry

21 pages. Title slightly changed, various minor corrections. To appear in Pure and Applied Mathematics Quarterly, volume dedic

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The maximal rank conjecture and rank two Brill-Noether theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The maximal rank conjecture and rank two Brill-Noether theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The maximal rank conjecture and rank two Brill-Noether theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-716774