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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > On symplectic hypersurfaces

## On symplectic hypersurfacesAdd to your list(s) Download to your calendar using vCal - Lehn, M (Mainz)
- Thursday 28 April 2011, 15:30-16:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Moduli Spaces The Grothendieck-Brieskorn-Slodowy theorem explains a relation between ADE -surface singularities $X$ and simply laced simple Lie algebras $g$ 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 $Sp N$. Moreover, the restriction of the characteristic map $i:g o g//G$ to $S$ is the semiuniversal deformation of $X$. We (j.w. Namikawa and Sorger) show that the theorem remains true for all non-regular nilpotent orbits if one considers Poisson deformations only. The situation is more complicated for non-simply laced Lie algebras. It is expected that holomorphic symplectic hypersurface singularities are rare. Besides the ubiquitous ADE -singularities we describe a four-dimensional series of examples and one six-dimensional example. They arise from slices to nilpotent orbits in Liealgebras of type $C_n$ and $G_2$. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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