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Generalizing the results of 1211.6077 and 1703.00905, we prove a formula forthe pushforward of an arbitrary analytic function of the exceptional divisorclass of a weighted blowup of an algebraic variety centered at a smoothcomplete intersection with normal crossing. We check this formula extensivelyby computing the generating function of intersection numbers of a weightedblowup of the generic SU(5) Tate model over arbitrary smooth base, andcomparing the answer to known results. Motivated by applications tofour-dimensional F-theory flux compactifications, we use our formula to computethe intersection pairing on the vertical part of the middle cohomology ofelliptic Calabi-Yau 4-folds resolving the generic F$_4$ and Sp(6) Tate modelswith non-minimal singularities. These resolutions lead to non-flat fibrationsin which certain fibers contain 3-fold (divisor) components, whose physicalinterpretation in M/F-theory remains to be fully explored.

Intersection Theory on Weighted Blowups of F-theory Vacua