Intersection cohomology of the moduli of of 1-dimensional sheaves and the moduli of Higgs bundles

Abstract: In general, the topology of the moduli space of semistable sheaves on an algebraic variety relies heavily on the choice of the Euler characteristic of the sheaves being parametrized. I will explain two situations where the intersection cohomology of the moduli space is independent of the choice of Euler characteristic: moduli of one-dimensional sheaves on toric Fano surfaces and moduli of Higgs bundles with poles. This confirms conjectures of Bousseau and Toda (in certain cases), which predicts that this independence should occur quite generally in the context of enumerative geometry of CY3-folds. Joint work with Junliang Shen.

algebraic geometry

Audience: researchers in the topic

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UC Davis algebraic geometry seminar