Back to Algebraic Geometry Seminar: Spring 2021
Algebraic Geometry Seminar
Date: Friday, Jan 29, 2021
Time: 3:30PM - 4:30PM
Location: Zoom
4 pm
Junliang Shen
MIT
Title |
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. We show a striking phenomenon that, for the moduli of 1-dimensional semistable sheaves on a toric del Pezzo surface (e.g. P^2), or the moduli of semistable Higgs bundles with respect to a divisor of degree > 2g-2 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 P^2, 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 work with Davesh Maulik. |
Algebraic Geometry