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

TL;DR

This paper characterizes the effective cone of certain moduli spaces of points on general curves, providing explicit descriptions and bounds, and introduces new geometric tools related to kernel bundles and syzygies.

Contribution

It offers a complete description of the effective cone of $C_{g-2}$ for general curves of genus $g \,\geq\, 6$, and introduces new bounds and characterizations involving kernel bundles.

Findings

Effective cone of $C_{g-2}$ fully described for $g \geq 6$

New bounds established for the effective cone of $C_{g-2m}$

Certain divisors characterized as subordinate loci related to kernel bundles

Abstract

We obtain a complete description of the effective cone of $C_{g-2}$ when $C$ is a general curve of genus $g \geq 6,$ 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.