Project page for virtual localization of stable log maps. relative-virtual-localization
- I think that a combination of “virtual localization revisited” and “virtual fundamental classes for derived stacks I” solves the virtual localization thing, which is great. Here’s an attempt to do it for the stable log maps moduli spaces. UPDATE: I was wrong, Prop B.6 and Cor B.7 in that paper requires an absolute POT.
After meeting with Bernd yesterday I learned that the derived localization stuff doesn’t give a relative localization formula. On the bright side this means I don’t have to learn more derived stuff right now.
Current approach: take the \(\mathfrak M(\mathcal X/B, \tau)\) spaces, split all edges so that only vertices remain to obtain a splitting \(\tilde\tau = (\tilde\tau_1,...,\tilde\tau_n)\) of types, resolve each \(\mathfrak M(\mathcal X/B, \tilde\tau_i)\) individually and then go back to \(\mathfrak M(\mathcal X/B, \tilde \tau)\) via the finite-to-one map \(\mathfrak M(\mathcal X/B, \tilde \tau) \to \prod_i \mathfrak M(\mathcal X/B, \tilde \tau_i)\) given in Proposition 5.4 of “Punctured Logarithmic Maps”.