Hitchin systems for invariant and anti-invariant vector bundles

Hacen Zelaci

Hitchin systems for invariant and anti-invariant vector bundles

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arxiv 1612.06910 v2 pith:G5LYW5TW submitted 2016-12-20 math.AG

Hitchin systems for invariant and anti-invariant vector bundles

Hacen Zelaci This is my paper

classification math.AG

keywords anti-invariantsystemsbundleshitchininvariantlocussigmavector

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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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