Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 090, 9 pages      arXiv:2108.02603      https://doi.org/10.3842/SIGMA.2021.090
Contribution to the Special Issue on Twistors from Geometry to Physics in honor of Roger Penrose

Spinors, Twistors and Classical Geometry

Nigel J. Hitchin
Mathematical Institute, Woodstock Road, Oxford, OX2 6GG, UK

Received August 07, 2021, in final form October 07, 2021; Published online October 10, 2021

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.

Key words: spinor; twistor; quadric; stable bundle.

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