Corpus ID: 119327005

Hitchin systems for invariant and anti-invariant vector bundles

  title={Hitchin systems for invariant and anti-invariant vector bundles},
  author={Hacen Zelaci},
  journal={arXiv: Algebraic Geometry},
  • Hacen Zelaci
  • Published 2016
  • Mathematics
  • arXiv: Algebraic Geometry
Given a smooth projective complex curve $X$ with an involution $\sigma$, we study the Hitchin systems for the locus of anti-invariant (resp. invariant) stable vector bundles over $X$ under $\sigma$. Using these integrable systems and the theory of the nilpotent cone, we study the irreducibility of these loci. The anti-invariant locus can be thought of as a generalisation of Prym varieties to higher rank. 
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