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SUMMARY:On symplectic hypersurfaces - Lehn\, M (Mainz)
DTSTART:20110428T143000Z
DTEND:20110428T153000Z
UID:TALK31019@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The Grothendieck-Brieskorn-Slodowy theorem explains a relation
  between ADE-surface singularities $X$ and simply laced simple Lie algebra
 s $g$ of the same Dynkin type: Let $S$ be a slice in $g$ to the subregular
  orbit in the nilpotent cone $N$. Then $X$ is isomorphic to $S
p N$. Moreo
 ver\, the restriction of the characteristic map $i:g	o g//G$ to $S$ is th
 e semiuniversal deformation of $X$. We (j.w. Namikawa and Sorger) show tha
 t the theorem remains true for all non-regular nilpotent orbits if one con
 siders Poisson deformations only. The situation is more complicated for no
 n-simply laced Lie algebras.\n\nIt is expected that holomorphic symplectic
  hypersurface singularities are rare. Besides the ubiquitous ADE-singulari
 ties we describe a four-dimensional series of examples and one six-dimensi
 onal example. They arise from slices to nilpotent orbits in Liealgebras of
  type $C_n$ and $G_2$.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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