Abstract
Building on our earlier work on toric residues and reduction, we give a proof of the mixed toric residue conjecture of Batyrev and Materov. We simplify and streamline our technique of tropical degenerations, which allows one to interpolate between two localization principles: one appearing in the intersection theory of toric quotients and the other in the calculus of toric residues. This quickly leads to the proof of the conjecture, which gives a closed formula for the summation of a generating series whose coefficients represent a certain naive count of the numbers of rational curves on toric complete intersection Calabi–Yau manifolds.
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