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SUMMARY:Schematic Harder Narasimhan stratification - Nitsure\, N (Tata Ins
 titute of Fundamental Research)
DTSTART:20110217T153000Z
DTEND:20110217T163000Z
UID:TALK29882@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The Harder Narasimhan type (in the sense of Gieseker semistabi
 lity) of a pure-dimensional coherent sheaf on a projective scheme is known
  to vary semi-continuously in a flat family\, which gives the well-known H
 arder Narasimhan stratification of the parameter scheme of the family\, by
  locally closed subsets.\nWe show that each stratum can be endowed with a 
 natural structure of a locally closed subscheme of the parameter scheme\, 
 which enjoys an appropriate universal property.\n\nAs an application\, we 
 deduce that pure-dimensional coherent sheaves of any given Harder Narasimh
 an type form an Artin algebraic stack.\n\nAs another application - jointly
  with L. Brambila-Paz and O. Mata - we describe moduli schemes for certain
  rank 2 unstable vector bundles on a smooth projective curve\, fixing some
  numerical data. \n\n
LOCATION:Seminar Room 1\, Newton Institute
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