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SUMMARY:Stratifications and coarse moduli spaces for Higgs bundles via Non
 -Reductive GIT
DTSTART:20191210T151500
DTEND:20191210T164500
DTSTAMP:20260509T193610Z
UID:acdc028e47f7ba0ea63da684c0bfefc60cfcd76d03c67266042e70ad
CATEGORIES:Conferences - Seminars
DESCRIPTION:Eloïse Hamilton (University of Oxford)\nThe moduli space of s
 emistable Higgs bundles on a smooth projective curve was first constructed
  by Nitsure in 1990\, using Geometric Invariant Theory (GIT). It is a wide
 ly studied moduli space thanks to its rich geometric structure. The aim of
  this talk is to describe how recent results in Non-Reductive GIT can be u
 sed to construct new moduli spaces of Higgs bundles\, including moduli spa
 ces of unstable Higgs bundles. More precisely\, I will describe two strati
 fications of the stack of Higgs bundles which satisfy the property that ea
 ch stratum admits a quasi-projective coarse moduli space. The first is a r
 efinement of the Higgs Harder-Narasimhan stratification (based on the inst
 ability type of a Higgs bundle)\, the second a refinement of the Harder-Na
 rasimhan stratification (based on the instability type of the underlying b
 undle). I will explicitly describe these refined stratifications in the ca
 se of rank 2 Higgs bundles\, and discuss the topology and geometry of the 
 corresponding moduli spaces.
LOCATION:GR A3 30 https://plan.epfl.ch/?room==GR%20A3%2030
STATUS:CONFIRMED
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