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Peer-reviewedCC BYJournal of Topology

Nontrivial Massey products on compact Kähler manifolds

  • Giovanni Placini1
  • Jonas Stelzig2
  • Leopold Zoller3
  1. 1Dipartimento di Matematica e Informatica Università degli Studi di Cagliari Cagliari Italy
  2. 2Mathematisches Institut der LMU München München Germany
  3. 3Facultat de Matemàtiques i Informàtica Universitat de Barcelona Barcelona Spain
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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.

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Cite

BibTeXRIS
BibTeX
@article{placini2026nontrivial,
  title = {{Nontrivial Massey products on compact Kähler manifolds}},
  author = {Giovanni Placini and Jonas Stelzig and Leopold Zoller},
  journal = {Journal of Topology},
  year = {2026},
  month = oct,
  doi = {10.1112/topo.70107},
  url = {https://doi.org/10.1112/topo.70107},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Nontrivial Massey products on compact Kähler manifolds
AU  - Giovanni Placini
AU  - Jonas Stelzig
AU  - Leopold Zoller
PY  - 2026
DA  - 2026/10/23
JO  - Journal of Topology
DO  - 10.1112/topo.70107
UR  - https://doi.org/10.1112/topo.70107
AB  - 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.
SN  - 1753-8416
SN  - 1753-8424
ER  -