Complex Manifolds (Feb 2019)

Algebraic Structure of Holomorphic Poisson Cohomology on Nilmanifolds

  • Poon Yat Sun,
  • Simanyi John

DOI
https://doi.org/10.1515/coma-2019-0004
Journal volume & issue
Vol. 6, no. 1
pp. 88 – 102

Abstract

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It is proved that on nilmanifolds with abelian complex structure, there exists a canonically constructed non-trivial holomorphic Poisson structure.We identify the necessary and sufficient condition for its associated cohomology to be isomorphic to the cohomology associated to trivial (zero) holomorphic Poisson structure. We also identify a sufficient condition for this isomorphism to be at the level of Gerstenhaber algebras.