Syzygy divisors on Hurwitz spaces

This paper, joint with A. Deopurkar, establishes divisor classes of generalizations of the Maroni loci in Hurwitz spaces. Each branched cover of the projective line determines, via the Casnati-Ekedahl-Schreyer relative canonical resolution, a whole bunch of vector bundles. Each bundle has a splitting type. If we impose that the splitting is not balanced then we sometimes determine a virtual divisor in the corresponding Hurwitz space. What are their divisor classes? This paper computes these classes, at least in partial compactifications of Hurwitz space, and we discover a curious phenomenon -- for fixed degree and genus, all of them are proportional! (An intrinsic explanation is still lacking.)