Nontrivial Massey products on compact Kähler manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916206706950144 |
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| author | Placini, Giovanni Stelzig, Jonas Zoller, Leopold |
| author_facet | Placini, Giovanni Stelzig, Jonas Zoller, Leopold |
| contents | We show that the bigraded quasi-isomorphism type of the bigraded, bidifferential algebra of forms on a compact Kähler manifold generally contains more information than the de Rham cohomology algebra with its real Hodge structure. More precisely, on any closed Riemann surface of genus at least two, there is a nontrivial ABC-Massey product. Furthermore, starting from dimension three, there are simply connected projective manifolds with a nonzero ABC-Massey product of three divisor classes. In particular, compact Kähler manifolds are generally not formal in the sense of pluripotential homotopy theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09867 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nontrivial Massey products on compact Kähler manifolds Placini, Giovanni Stelzig, Jonas Zoller, Leopold Algebraic Topology Algebraic Geometry Differential Geometry We show that the bigraded quasi-isomorphism type of the bigraded, bidifferential algebra of forms on a compact Kähler manifold generally contains more information than the de Rham cohomology algebra with its real Hodge structure. More precisely, on any closed Riemann surface of genus at least two, there is a nontrivial ABC-Massey product. Furthermore, starting from dimension three, there are simply connected projective manifolds with a nonzero ABC-Massey product of three divisor classes. In particular, compact Kähler manifolds are generally not formal in the sense of pluripotential homotopy theory. |
| title | Nontrivial Massey products on compact Kähler manifolds |
| topic | Algebraic Topology Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2404.09867 |