Localization Statement To Prove

Proposition

Let \(\mathcal M\) be the moduli space of basic stable log maps to toric variety \(X\). Then \[[\mathcal M]^{vir} = e\left(N^{vir}_{\mathcal M^T/\mathcal M}\right)\frown [\mathcal M^T]^{vir}\]

  • what is \(N^{vir}_{\mathcal M^T/\mathcal M}\)?
  • which Chow ring does this take place in?
  • which notion of the fixed stack \(\mathcal M^T\) is being used?