Higher rank Brill-Noether theory on sections of K3 surfaces

Details Higher rank Brill-Noether theory on sections of K3 surfaces Higher rank Brill-Noether theory on sections of K3 surfaces

2011-02-01

arxiv.org/abs/1102.0276v3

Mathematics

Algebraic Geometry

15 pages. Final version, to appear in the International Journal of Mathematics

Scientific paper

We discuss the role of K3 surfaces in the context of Mercat's conjecture in higher rank Brill-Noether theory. Using liftings of Koszul classes, we show that Mercat's conjecture in rank 2 fails for any number of sections and for any gonality stratum along a Noether-Lefschetz divisor inside the locus of curves lying on K3 surfaces. Then we show that Mercat's conjecture in rank 3 fails even for curves lying on K3 surfaces with Picard number 1. Finally, we provide a detailed proof of Mercat's conjecture in rank 2 for general curves of genus 11, and describe explicitly the action of the Fourier-Mukai involution on the moduli space M_{11}.

Affiliated with

Also associated with

No associations

Rating

Higher rank Brill-Noether theory on sections of K3 surfaces 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 Higher rank Brill-Noether theory on sections of K3 surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Higher rank Brill-Noether theory on sections of K3 surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-79115