Spinors, Twistors and Classical Geometry

TL;DR

This paper explores the Hitchin system on stable rank 2 bundles in genus 2 and 3, linking the geometry of quadrics to Penrose's twistor spaces and classical geometric results.

Contribution

It provides explicit analysis of the Hitchin system's restriction to Higgs fields and connects classical geometry with twistor theory through families of quadrics.

Findings

Relation between quadrics and Penrose's twistor spaces

Explicit description of Hitchin system on stable bundles

Connections to classical geometric results

Abstract

The paper studies explicitly the Hitchin system restricted to the Higgs fields on a fixed very stable rank 2 bundle in genus 2 and 3. The associated families of quadrics relate to both the geometry of Penrose's twistor spaces and several classical results.