Syzygy divisors on Hurwitz spaces

Abstract

We describe a sequence of effective divisors on the Hurwitz space Hd,g for d dividing g 1 and compute their cycle classes on a partial cornpactification. 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. These computations are motivated by the question of determining the effective cone and ultimately the birational type of H-d,H-g. Show more