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SUMMARY:Eloise Hamilton (IMJ-PRG\, University of Paris)
DTSTART:20201112T130000Z
DTEND:20201112T143000Z
DTSTAMP:20260423T005800Z
UID:AGNTISTA/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AGNTISTA/14/
 ">Moduli spaces for unstable Higgs bundles of rank 2 and their geometry</a
 >\nby Eloise Hamilton (IMJ-PRG\, University of Paris) as part of Algebraic
  Geometry and Number Theory seminar - ISTA\n\n\nAbstract\nThe moduli space
  of semistable Higgs bundles of arbitrary rank and degree on a nonsingular
  projective curve was first constructed by Nitsure in 1990\, using Geometr
 ic Invariant Theory (GIT). Thanks to its rich geometric structure\, this m
 oduli 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 us
 ed to construct moduli spaces for Higgs bundles which are not semistable\,
  and to describe initial steps towards the study of their geometry in the 
 rank 2 case.  In the first part of the talk we will start by giving a summ
 ary of Nitsure's GIT construction of the moduli space and describing the m
 ain geometric features of the moduli space. We will then consider the spec
 ial 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 over a smooth pro
 jective curve of arbitrary genus. We will then describe how the geometry o
 f these moduli spaces can be studied in the rank 2 case\, using the Higgs 
 field scaling C-star action on the one hand\, and their construction as No
 n-Reductive GIT quotients on the other.\nQr image\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/14/
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