Syzygy divisors on Hurwitz spaces

Abstract

We describe a sequence of effective divisors on the Hurwitz space $H_{d,g}$ for $d$ dividing $g-1$ and compute their cycle classes on a partial compactification. These divisors arise from vector bundles of syzygies canonically associated to a branched cover. We find that the cycle classes are all proportional to each other.

13 pages. For the issue of Contemporary Mathematics titled "Higher genus curves in mathematical physics and arithmetic geometry."