Hypertoric Hitchin Systems and Kirchhoff Polynomials

Hitchin systems on ll-curves

Hitchin Systems at Low Genera

The paper gives a quick account of the simplest cases of the Hitchin integrable systems and of the Knizhnik-Zamolodchikov-Bernard connection at genus 0, 1 and 2. In particular, we construct the action-angle variables of the genus 2 Hitchin system with group SL2 by exploiting its relation to the classical Neumann integrable systems. 1 Hitchin systems As was realized by Hitchin in [16], a large f...

Hitchin systems in N = 2 field theory

This note is a short review of the way Hitchin systems appear in four-dimensional N = 2 supersymmetric field theory. The literature on the Hitchin system and its role in quantum field theory is a vast one. Restricting attention just to the role of Hitchin systems in N = 2 supersymmetric field theory (thus neglecting such fascinating topics as T-duality on the Hitchin fibration and its relation ...

Donagi-markman Cubic for Hitchin Systems

The Donagi-Markman cubic is the differential of the period map for algebraic completely integrable systems. Here we prove a formula for the cubic in the case of Hitchin’s system for arbitrary semisimple g. This was originally stated (without proof) by Pantev for sln.

The hypertoric intersection cohomology ring

We present a functorial computation of the equivariant intersection cohomology of a hypertoric variety, and endow it with a natural ring structure. When the hyperplane arrangement associated with the hypertoric variety is unimodular, we show that this ring structure is induced by a ring structure on the equivariant intersection cohomology sheaf in the equivariant derived category. The computati...