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      On the intersection cohomology of the moduli of \(\mathrm{SL}_n\)-Higgs bundles on a curve

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          Abstract

          We explore the cohomological structure for the (possibly singular) moduli of \(\mathrm{SL}_n\)-Higgs bundles for arbitrary degree on a genus g curve with respect to an effective divisor of degree >2g-2. We prove a support theorem for the \(\mathrm{SL}_n\)-Hitchin fibration extending de Cataldo's support theorem in the nonsingular case, and a version of the Hausel-Thaddeus topological mirror symmetry conjecture for intersection cohomology. This implies a generalization of the Harder-Narasimhan theorem concerning semistable vector bundles for any degree. Our main tool is an Ng\^{o}-type support inequality established recently which works for possibly singular ambient spaces and intersection cohomology complexes.

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          Journal
          01 March 2021
          Article
          2103.01285
          ae59528f-16e5-4c58-9721-785ffa392f88

          http://creativecommons.org/licenses/by/4.0/

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          22 pages. Comments are welcome
          math.AG

          Geometry & Topology
          Geometry & Topology

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