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Generalized deformations and holomorphic Poisson cohomology of solvmanifolds

Authors
  • Kasuya, Hisashi1
  • 1 Tokyo Institute of Technology, Department of Mathematics, 1-12-1, O-okayama, Meguro, Tokyo, 152-8551, Japan , Meguro (Japan)
Type
Published Article
Journal
Annals of Global Analysis and Geometry
Publisher
Springer Netherlands
Publication Date
Sep 22, 2016
Volume
51
Issue
2
Pages
155–177
Identifiers
DOI: 10.1007/s10455-016-9529-x
Source
Springer Nature
Keywords
License
Yellow

Abstract

We describe the generalized Kuranishi spaces of solvmanifolds with left-invariant complex structures. By using such description, we study the stability of left-invariantness of deformed generalized complex structures and smoothness of generalized Kuranishi spaces on certain classes of solvmanifolds. We also give explicit finite-dimensional cochain complexes which computes the holomorphic Poisson cohomology of nilmanifolds and solvmanifolds.

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