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Seminar of Algebraic Geometry in East Asia
9:00 - 10:00, January 8, 2021 (Friday)
Lecture Hall 5F, Cosmology Building, NTU
(臺灣大學宇宙學大樓 五樓演講廳)
Intersection Cohomology of the Moduli of 1-dimensional Sheaves and the Moduli of Higgs Bundles
Junliang Shen (Massachusetts Institute of Technology)


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. We show a striking phenomenon that, for the moduli of 1-dimensional semistable sheaves on a toric del Pezzo surface (e.g. ) or the moduli of semistable Higgs bundles with respect to a divisor of degree > on a curve, the intersection cohomology (together with the perverse and the Hodge filtrations) of the moduli space is independent of the choice of the Euler characteristic. This confirms a conjecture of Bousseau for , and proves a conjecture of Toda in the case of certain local Calabi-Yau 3-folds. In the proof, a generalized version of Ngô's support theorem plays a crucial role. Based on joint with Davesh Maulik.


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