Virtual Normal Bundle

Consider the moduli space of stable maps \(\overline{\mathcal M}(X,D)\) equipped with a \(\mathbb C^*\) action inherited from \(X\), let \(\Gamma\) be a graph representing the connected component \(\overline{\mathcal M}_{\Gamma}(X,D)\) of the fixed locus of \(\overline{\mathcal M}(X,D)\). Then the virtual normal bundle of \(\overline{\mathcal M}_{\Gamma}(X,D)\), denoted \(N_\Gamma\), is the moving (i.e. the non-torus fixed) part of the obstruction theory.

See this paper of [BROKEN LINK: pdf:/Users/isaac/notes/lib/papers/graber-vakil_virtual-localization.pdf::1] for a little bit of discourse on it.