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SUMMARY:Junliang Shen (MIT)
DTSTART:20201204T163000Z
DTEND:20201204T173000Z
DTSTAMP:20260423T010337Z
UID:UBC-AG/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UBC-AG/10/">
 Intersection cohomology of the moduli of of 1-dimensional sheaves and the 
 moduli of Higgs bundles</a>\nby Junliang Shen (MIT) as part of UBC Vancouv
 er Algebraic Geometry Seminar\n\n\nAbstract\nIn general\, the topology of 
 the moduli space of semistable sheaves on an algebraic variety relies heav
 ily on the choice of the Euler characteristic of the sheaves. We show a st
 riking phenomenon that\, for the moduli of 1-dimensional semistable sheave
 s on a toric del Pezzo surface (e.g. P^2) or the moduli of semistable Higg
 s bundles with respect to a divisor of degree > 2g-2 on a curve\, the inte
 rsection cohomology of the moduli space is independent of the choice of th
 e Euler characteristic.  This confirms a conjecture of Bousseau for P^2\, 
 and proves a conjecture of Toda in the case of local toric Calabi-Yau 3-fo
 lds. In the proof\, a generalized version of Ngô's support theorem plays 
 a crucial role. Based on joint work in progress with Davesh Maulik.\n
LOCATION:https://researchseminars.org/talk/UBC-AG/10/
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