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math.AGSep 7, 2021
2
citations (OpenAlex)
authors
  • Yat Sun Poon
institutions
  • University of California, Riverside
arXiv abstractPDF
paper

Abelian Complex Structures and Generalizations

arXiv:2109.03353 · doi:10.1515/coma-2020-0117

Abstract

After a review on the development of deformation theory of abelian complex structures from both the classical and generalized sense, we propose the concept of semi-abelian generalized complex structure. We present some observations on such structure and illustrate this new concept with a variety of examples.

References in corpus (11)

  • Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields
  • Instantons, Poisson structures and generalized Kaehler geometry
  • Geometry of nilmanifolds with left-invariant complex structure and deformations in the large
  • Classification of abelian complex structures on 6-dimensional Lie algebras
  • Lie-algebra Dolbeault cohomology and small deformations of nilmanifolds
  • Poisson modules and degeneracy loci
  • Formality in generalized Kahler geometry
  • Weak Mirror Symmetry of Complex Symplectic Algebras
  • Constructions and classifications of projective Poisson varieties
  • A Hodge-Type Decomposition of Holomorphic Poisson Cohomology on Nilmanifolds
  • Cohomologies of generalized complex manifolds and nilmanifolds
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