Kernel Bundles, Syzygies Of Points, and The Effective Cone of C_{g-2}

Abstract

We obtain a complete description of the effective cone of $C_{g-2}$ when $C$ is a general curve of genus $g\ge 6,$ as well as a new bound in the case where $C$ is a smooth plane quintic. In addition, we obtain a new virtual bound for the effective cone of $C_{g-2m}$ which is a genuine bound when $m=2,$ and we also characterize certain natural divisors on $C_{g-2}$ as subordinate loci associated to adjunctions of kernel bundles.

arXiv commentThis is a substantial revision. Proposition III has been modified to account for a gap in the original statement, and the section on the plane quintic case has been thoroughly rewritten. To appear in International Mathematics Research Notices

References in corpus (1)

• Geometry of curves with exceptional secant planes: linear series along the general curve