## Hitchin systems for invariant and anti-invariant vector bundles

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## 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.## References

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## Additional Information

**Zelaci Hacen**- Affiliation: Department of Mathematics, El-Oued University, El-Oued, Algeria
- MR Author ID: 1243503
- ORCID: 0000-0001-6995-9859
- Email: z.hacen@gmail.com
- Received by editor(s): April 12, 2018
- Received by editor(s) in revised form: November 10, 2020, August 1, 2021, and November 17, 2021
- Published electronically: February 4, 2022
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**375**(2022), 3665-3711 - MSC (2020): Primary 14H60, 14H40, 14H70
- DOI: https://doi.org/10.1090/tran/8599
- MathSciNet review: 4402672