Spinors, Twistors and Classical Geometry - Hitchin, Nigel J. (Symmetry, Integrability and Geometry: Methods and Applications, 2021)
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.