Nilpotent orbits and Hilbert schemes

Details Nilpotent orbits and Hilbert schemes Nilpotent orbits and Hilbert schemes

2007-01-31

arxiv.org/abs/math/0701909v1

Mathematics

Symplectic Geometry

Scientific paper

We construct embeddings $\mathcal{Y}_{n,\tau} \to {Hilb}^n (\Sigma_{\tau})$ for each of the classical Lie algebras $\ger{sp}_{2m}(\Cc)$, $\ger{so}_{2m}(\Cc)$, and $\ger{so}_{2m+1}(\Cc)$. The space $\mathcal{Y}_{n,\tau}$ is the fiber over a point $\tau \in \ger h / W$ of the restriction of the adjoint quotient map $\chi : \ger g \to \ger h /W$ to a suitably chosen transverse slice of a nilpotent orbit. These embeddings were discovered for $\ger{sl}_{2m}(\Cc)$ by Ciprian Manolescu. They are related to the symplectic link homology of Seidel and Smith.

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