Singularity Properties of Graph Varieties

Abstract

For a graph $G=(V,E)$, and a symplectic vector space $(W,⟨\cdot ,\cdot ⟩)$, we define a variety $X(G,W)$ 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.