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arXiv · 2406.00931

Cohomological splitting over rationally connected bases

Shaoyun Bai·Daniel Pomerleano·Guangbo Xu
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Abstract

We prove a cohomological splitting result for Hamiltonian fibrations over enumeratively rationally connected symplectic manifolds As a key application, we prove that the cohomology of a smooth, projective family over a smooth (stably) rational projective variety splits additively over any field. The main ingredients in our arguments include the theory of Fukaya-Ono-Parker (FOP) perturbations developed by the first and third author, which allows one to define integer-valued Gromov-Witten type invariants, and variants of Abouzaid-McLean-Smith's global Kuranishi charts tailored to concrete geometric problems.

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Shaoyun Bai, Daniel Pomerleano, Guangbo Xu. 2024-06-03. Cohomological splitting over rationally connected bases. https://arxiv.org/abs/2406.00931

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