Hitchin systems for invariant and anti-invariant vector bundles

Hacen, Zelaci

doi:10.1090/tran/8599

Hitchin systems for invariant and anti-invariant vector bundles
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Trans. Amer. Math. Soc. 375 (2022), 3665-3711 Request permission

Abstract:

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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