Room 515, Cosmology Building, NTU
(臺灣大學次震宇宙館 515研討室)
Intersection Cohomology of the Moduli of 1-dimensional Sheaves and the Moduli of Higgs Bundles
Junliang Shen (Massachusetts Institute of Technology)
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. 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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