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SUMMARY:Emilio Franco (IST Lisboa)
DTSTART:20210519T183000Z
DTEND:20210519T200000Z
DTSTAMP:20260423T021708Z
UID:BRAG/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BRAG/46/">De
 formation theory for orthogonal and symplectic sheaves</a>\nby Emilio Fran
 co (IST Lisboa) as part of Brazilian algebraic geometry seminar\n\n\nAbstr
 act\nModuli spaces of principal bundles usually carry interesting\ngeometr
 ic structures\, being a powerful\, and often unique\, source of\nexamples 
 of varieties with prescribed properties and characteristics.\nNevertheless
 \, these spaces might be non-compact whenever the base\n(smooth) scheme ha
 s dimension higher than 1. Principal sheaves provide a\nnatural compactifi
 cation of the moduli space of principal bundles for a\nconnected complex r
 eductive structure group. Therefore\, moduli spaces of\nprincipal sheaves 
 are projective varieties equipped with an interesting\ngeometry\, at least
 \, on a dense subset. In order to check whether or not\nthese properties e
 xtend to the compactification\, we need a local\ndescription of the moduli
  spaces\, precisely over the locus where the\nprincipal sheaves fail to be
  principal bundles. Such description would\nnaturally derive from deformat
 ion theory of principal sheaves\, which is\nstill missing at present date.
 \n\nIn this talk we consider orthogonal and symplectic sheaves\, and show\
 nthat the deformation and obstruction theory of these objects is\ncontroll
 ed by a deformation complex naturally built out of our starting\northogona
 l (resp. symplectic) sheaf.\n
LOCATION:https://researchseminars.org/talk/BRAG/46/
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