Cohomological splitting over rationally connected bases
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...
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| creator | Bai, Shaoyun Pomerleano, Daniel Xu, Guangbo |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.2406.00931 |
| format | Article |
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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
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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
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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.</abstract><doi>10.48550/arxiv.2406.00931</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Algebraic Geometry Mathematics - Symplectic Geometry |
| title | Cohomological splitting over rationally connected bases |
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