Intersection Theory on Weighted Blowups of F-theory Vacua
Apr 29, 2023Citations per year
0 Citations
Abstract: (arXiv)
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 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.Note:
- 37 pages plus an appendix. v2: Minor clarifications to Sections 3 and 4
- compactification: flux
- F-theory
- space: Calabi-Yau
- algebra
- cohomology
- vacuum state: flux
- singularity
- fibre bundle
- SU(5)
References(75)
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