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We determine the cycle classes of effective divisors in the compactified Hurwitz spaces of curves of genus g with a linear system of degree d that extend the Maroni divisors on the open Hurwitz space. Our approach uses Chern classes associated to a global-to-local evaluation map of a vector bundle over a generic $P^1$-bundle over the Hurwitz space.
The Maroni stratification on the Hurwitz space of degree $d$ covers of genus $g$ has a stratum that is a divisor only if $d-1$ divides $g$. Here we construct a stratification on the Hurwitz space that is analogous to the Maroni stratification, but ha
Let V be a convex vector bundle over a smooth projective manifold X, and let Y be the subset of X which is the zero locus of a regular section of V. This mostly expository paper discusses a conjecture which relates the virtual fundamental classes of
An MBM locus on a hyperkahler manifold is the union of all deformations of a minimal rational curve with negative self-intersection. MBM loci can be equivalently defined as centers of bimeromorphic contractions. It was shown that the MBM loci on defo
Given a smooth and separated K(pi,1) variety X over a field k, we associate a cycle class in etale cohomology with compact supports to any continuous section of the natural map from the arithmetic fundamental group of X to the absolute Galois group o
Let F denote a homogeneous degree 4 polynomial in 3 variables, and let s be an integer between 1 and 5. We would like to know if F can be written as a sum of fourth powers of s linear forms (or a degeneration). We determine necessary and sufficient c