Singularity Properties of Graph Varieties

For a graph $G=(V,E)$, and a symplectic vector space $(W, \left<\cdot,\cdot\right>)$,wedefineavariety$X(G,W)$ consisting of all functions $w:V\to W$ satisfying $<w(u),w(v)>=0$ for any edge $\{u,v\}$ in $G$. We study the singularities of this varieties.