5 citations · 8 across the 8 of their papers we have counts for
8 papers
Linear series and existence of branched covers
Brian Osserman
In this paper, we use the perspective of linear series, and in particular results following from the degeneration tools of limit linear series, to give a number of new results on e…
Deformations of covers, Brill-Noether theory, and wild ramification
Brian Osserman
In this paper, we give a simple description of the deformations of a map between two smooth curves with partially prescribed branching, in the cases that both curves are fixed, and…
The generalized Verschiebung map for curves of genus 2
Brian Osserman
Let C be a smooth curve, and M_r(C) the coarse moduli space of vector bundles of rank r and trivial determinant on C. We examine the generalized Verschiebung map V_r: M_r(C^(p)) --…
Mochizuki's crys-stable bundles: a lexicon and applications
Brian Osserman
Mochizuki's work on torally crys-stable bundles has extensive implications for the theory of logarithmic connections on vector bundles of rank 2 on curves, once the language is tra…
Frobenius-unstable bundles and p-curvature
Brian Osserman
We use the theory of p-curvature of connections to analyze stable vector bundles of rank 2 on curves of genus 2 which pull back to unstable bundles under the Frobenius morphism. We…
Logarithmic connections with vanishing p-curvature
Brian Osserman
We examine logarithmic connections with vanishing p-curvature on smooth curves by studying their kernels, describing them in terms of formal local decomposition. We then apply our…