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DTSTART:20180325T030000
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DTSTAMP:20231002T081637Z
UID:5936c1704182b825016861@ist.ac.at
DTSTART:20180301T130000
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DESCRIPTION:Speaker: Tristan Bozec\nhosted by Tamas Hausel\nAbstract: Given
a curve X of genus g\, the moduli stack of Higgs sheaves of rank r and de
gree d is known to be of dimension 2(g-1)r^2. It can be viewed as the cota
ngent stack of the stack of coherent sheaves of type (r\,d) over X\, and L
aumon proved that the substack of nilpotent Higgs pairs is Lagrangian. Thi
s substack is a global analog of the nilpotent cone\, and is nothing but t
he 0-fiber of the Hitchin map. It is highly singular\, and one first inter
esting step toward its comprehension is the study of its irreducible compo
nents. This study is also motivated by a result stating that the number of
stable components is given by the value at 1 of the Kac polynomial of the
quiver with one vertex and g loops (conjectured by Hausel\, Letellier\, R
odriguez Villegas\, proved by Mellit)\, as well as by the W=P conjecture (
de Cataldo\, Hausel\, Migliorini). I will give a nice combinatorial descri
ption of this set of components\, and will explain which ones subsist when
we restrict ourselves to the semistable locus (with respect to the usual
slope stability).
LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS
TA
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Tristan Bozec: Irreducible components of the global nilpotent cone
URL:https://talks-calendar.ista.ac.at/events/1032
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