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DTSTAMP:20260406T041148Z
UID:1605186000@ist.ac.at
DTSTART:20201112T140000
DTEND:20201112T153000
DESCRIPTION:Speaker: Eloise Hamilton\nhosted by Tamas Hausel\nAbstract: The
  moduli space of semistable Higgs bundles of arbitrary rank and degree on 
 a nonsingular projective curve was first constructed by Nitsure in 1990\, 
 using Geometric Invariant Theory (GIT). Thanks to its rich geometric struc
 ture\, this moduli space continues to represent an active area of research
 . The aim of this talk is to describe how recent results in Non-Reductive 
 GIT can be used to construct moduli spaces for Higgs bundles which are not
  semistable\, and to describe initial steps towards the study of their geo
 metry in the rank 2 case.  In the first part of the talk we will start by
  giving a summary of Nitsure's GIT construction of the moduli space and de
 scribing the main geometric features of the moduli space. We will then con
 sider the special case of (twisted) Higgs bundles over the projective line
 \, in order to introduce unstable Higgs bundles and their moduli spaces in
  an elementary way. In the second part of the talk we will sketch the Non-
 Reductive GIT construction of moduli spaces for unstable Higgs bundles ove
 r a smooth projective curve of arbitrary genus. We will then describe how 
 the geometry of these moduli spaces can be studied in the rank 2 case\, us
 ing the Higgs field scaling C-star action on the one hand\, and their cons
 truction as Non-Reductive GIT quotients on the other.
LOCATION:https://mathseminars.org/seminar/AGNTISTA\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Eloise Hamilton: Moduli spaces for unstable Higgs bundles of rank 2
  and their geometry
URL:https://talks-calendar.ista.ac.at/events/2950
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