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arXiv · 2305.00297

Intersection Theory on Weighted Blowups of F-theory Vacua

Veronica Arena·Patrick Jefferson·Stephen Obinna
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Abstract

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

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Veronica Arena, Patrick Jefferson, Stephen Obinna. 2023-04-29. Intersection Theory on Weighted Blowups of F-theory Vacua. https://arxiv.org/abs/2305.00297

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