134 citations · 232 across the 19 of their papers we have counts for
20 papers
Abelian Complex Structures and Generalizations
Yat Sun Poon
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 generali…
Frobenius Structures and Generalized Deformation of Kodaira Manifolds
Yat Sun Poon
It is known that generalized deformation in the sense of Hitchin-Gaultieri is a geometric realization of the degree-2 component of Kontsevich-Barannikov's homological approach to e…
Algebraic Structure of Holomorphic Poisson Cohomology on Nilmanifolds
Yat Sun Poon, John Simanyi
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 su…
A Hodge-Type Decomposition of Holomorphic Poisson Cohomology on Nilmanifolds
Yat Sun Poon, John Simanyi
A cohomology theory associated to a holomorphic Poisson structure is the hypercohomology of a bi-complex where one of the two operators is the classical -operato…
Degeneracy of Holomorphic Poisson Spectral Sequence
Yat Sun Poon
Through the theory of Lie bi-algebroids and generalized complex structures, one could define a cohomology theory naturally associated to a holomorphic Poisson structure. It is know…
Holomorphic Poisson Structures and its Cohomology on Nilmanifolds
Zhuo Chen, Anna Fino, Yat-Sun Poon
The subject for investigation in this note is concerned with holomorphic Poisson structures on nilmanifolds with abelian complex structures. As a basic fact, we establish that on s…