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These are the adjoint orbits of a complex semisimple group lying in the nilpotent cone. Nilpotent orbits arise in algebraic geometry, symplectic geometry, and representation theory.

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Nilpotent orbits and mixed Hodge structures

Let $(H_\mathbb{Z}, \{h^{p,q}\}_{p+q=n}, \phi)$ be the datum to define weight $n$ polarized Hodge structures on $H_\mathbb{Z}$, $h^{p,q}$ is the Hodge numbers, $\phi$ is a polarization. Let $D$ be the …
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