ScalingStacks

Proposition 3.35 . [04C3]

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Proposition 3.35.

(Moduli space integral formula) The Solomon functional 𝒮⁡(L)\mathcal{S}(L) is the integral of the following complex valued volume form over the (n−1)(n-1)-dimensional moduli spaces of holomorphic curves:

𝒮⁡(L)=∫ℳℐ,ℐ=Im​∫Σe−i​θ^​F​ω+Im​∑all cornerse−i​θ^​F​f|−+.\mathcal{S}(L)=\int_{\mathcal{M}}\mathcal{I},\quad\mathcal{I}=\text{Im}\int_{\Sigma}e^{-i\hat{\theta}}F\omega+\text{Im}\sum_{\text{all corners}}e^{-i\hat{\theta}}Ff|^{+}_{-}. (39)

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