Restricted Lazarsfeld-Mukai bundles and canonical curves
Algebraic Geometry
2014-10-06 v1
Abstract
We prove two results. First, we establish that the normal bundle of any smooth curve of genus 7 having maximal Clifford index is stable. Note that 7 is the smallest genus for which such a result could possibly hold. We then show that rank four Lazarsfeld-Mukai vector bundles on a curve that lies on a general K3 surface are stable. Both results have consequences for Mercat's conjecture on higher rank vector bundles on generic curves.
Keywords
Cite
@article{arxiv.1410.0857,
title = {Restricted Lazarsfeld-Mukai bundles and canonical curves},
author = {Marian Aprodu and Gavril Farkas and Angela Ortega},
journal= {arXiv preprint arXiv:1410.0857},
year = {2014}
}
Comments
15 pages. Section 2 of this paper is taken from our preprint arXiv:1212.6248, which has been divided in two parts. To appear in a volume of Advanced Studies in Pure Mathematics (Math. Soc. Japan) on the occasion of Mukai's 60th birthday