Journal of Topology· 2026Q1
Nontrivial Massey products on compact Kähler manifolds
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- Q1SCImago
- 2026year
Short summary
Compact Kähler manifolds are generally not formal in the sense of pluripotential homotopy theory, as evidenced by the existence of nontrivial Massey products.
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Key points
- Compact Kähler manifolds are generally not formal in pluripotential homotopy theory.
- A nontrivial -Massey product exists on compact Kähler manifolds fibering over a Riemann surface of genus >= 2.
- Simply connected projective manifolds of dimension three or higher can possess a nonzero -Massey product of three divisor classes.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract By a result of Deligne, Griffiths, Morgan, and Sullivan, compact Kähler manifolds are rationally formal. In contrast to this, we show that the pluripotential 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 compact Kähler manifold fibering over a Riemann surface of genus at least two, there is a nontrivial ‐Massey product. Furthermore, starting from dimension three, there are simply connected projective manifolds with a nonzero ‐Massey product of three divisor classes. In particular, compact Kähler manifolds are generally not formal in the sense of pluripotential homotopy theory.
The authors' abstract, as published at the source. Journal of Topology, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics