Support Theorems for Algebraic Maps

We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for GL n {\mathrm{GL}_{n}} over the locus of reduced spectral curves. In contrast to the case of meromorphic Higgs fields we find additional supports at the loci of reducible spectral curves. Their contribution to the global cohomology is governed by a finite twist of Hitchin fibrations for Levi subgroups. The corresponding summands give non-trivial contributions to the cohomology of the moduli spaces for every n ≥ 2 {n\geq{2}} . A key ingredient is a restriction result for intersection cohomology sheaves that allows us to compare the fibration to the one defined over versal deformations of spectral curves.

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Supports for linear degenerations of flag varieties

Fang

Reineke

2021

Doc. Math.

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Support Theorems for Algebraic Maps

Abstract: We review some recent progress on the topological properties of algebraic maps, with special emphasis on the determination of the "supports" of a map.

Cited by 3 publications

References 33 publications

Nakajima's quiver varieties and triangular bases of rank-2 cluster algebras

Nakajima's quiver varieties and triangular bases of rank-2 cluster algebras

A support theorem for\break the Hitchin fibration: The case of GL_n and K_C

Supports for linear degenerations of flag varieties

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Support Theorems for Algebraic Maps

Abstract: We review some recent progress on the topological properties of algebraic maps, with special emphasis on the determination of the "supports" of a map.

Cited by 3 publications

References 33 publications

Nakajima's quiver varieties and triangular bases of rank-2 cluster algebras

Nakajima's quiver varieties and triangular bases of rank-2 cluster algebras

A support theorem for\break the Hitchin fibration: The case of GL n and K C

Supports for linear degenerations of flag varieties

Contact Info

Product

Resources

About

A support theorem for\break the Hitchin fibration: The case of GL_n and K_C