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9 papers · 2 filters
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…
An elliptic K3 surface associated to Heron triangles
Ronald van Luijk
A rational triangle is a triangle with rational sides and rational area. A Heron triangle is a triangle with integral sides and integral area. In this article we will show that the…
A K3 surface associated to certain integral matrices with integral eigenvalues
Ronald van Luijk
In this article we will show that there are infinitely many symmetric, integral 3 x 3 matrices, with zeros on the diagonal, whose eigenvalues are all integral. We will do this by p…
Polynomial recurrences and cyclic resultants
Christopher J. Hillar, Lionel Levine
Let be an algebraically closed field of characteristic zero and let . The -th {\it cyclic resultant} of is \[r_m = \text{Res}(f,x^m-1).\] A generic monic pol…
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…
Del Pezzo surfaces of degree 6
Patrick Corn
We give a correspondence which associates, to any Del Pezzo surface X of degree 6 over a field k of characteristic 0, a collection of data consisting of a Severi-Brauer variety/k a…