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UID:8144@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20150309T140000
DTEND;TZID=Europe/Paris:20150309T150000
DTSTAMP:20241120T210043Z
URL:https://www.i2m.univ-amu.fr/evenements/git-characterizations-of-harder
 -narasimhan-filtrations/
SUMMARY:Alfonso Zamora (...): GIT characterizations of Harder-Narasimhan fi
 ltrations
DESCRIPTION:Alfonso Zamora: We will discuss constructions of moduli spaces 
 in algebraic geometry by using Geometric Invariant Theory (GIT).\nWhen per
 forming such constructions we usually impose a notion of stability for the
  objects we want to classify and another notion of GIT stability appears\,
  then it is shown that both notions coincide. For an object which is unsta
 ble (i.e. contradicting the stability condition) there exists a unique can
 onical filtration\, called the Harder-Narasimhan filtration. Onthe other h
 and\, GIT stability is checked by 1-parameter subgroups by the classical H
 ilbert-Mumford criterion\, and it turns out that there exists a unique 1-p
 arameter subgroup giving a notion of maximal unstability in the GIT sense.
  We show how to prove that this special 1-parameter subgroup can be conver
 ted into a filtration of the object and coincides with the Harder-Narasimh
 an filtration\, hence both notions of maximal unstability are the same. We
  will present the correspondence for the moduli problem of classifying coh
 erent sheaves on a smooth complex projective variety. A similar treatment 
 can be used to prove the analogous result for other moduli problems: holom
 orphic pairs\, Higgs sheaves\, rank 2 tensors and finite dimensional quive
 r representations. Finally\, we will talk about work in progress: extendin
 g the results to principal bundles.\n\n\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Alfonso_Zamora.jpg
CATEGORIES:Séminaire,Dynamique et Topologie
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DTSTART:20141026T020000
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