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Chunghoon Kim

Publications and source records attributed to Chunghoon Kim.

7 recordsLinked to original sources
arXiv2015

Theorem of existence and completeness for holomorphic Poisson structures

In this paper, we define a concept of a family of compact holomorphic Poisson manifolds on the basis of Kodaira-Spencer's deformation theory and deduce the integrability condition. We prove an analogue of their `Theorem of existence for complex analytic structures' under some analytic assumption, and establish an analogue of their `Theorem of completeness for complex analytic structures' in the context of holomorphic Poisson deformations.

math.AG↗
arXiv2015

Deformations of holomorphic Poisson maps

In this paper, we study deformations of holomorphic Poisson maps which extend Horikawa's series of papers on deformations of holomorphic maps in the context of holomorphic Poisson deformations. In appendices, we present deformations of Poisson morphisms in the language of functors of Artin rings which is the algebraic version of deformations of holomorphic Poisson maps. We identity first-order deformations and obstructions.

math.AG↗
arXiv2015

Deformations of compact holomorphic Poisson submanifolds

In this paper, we study deformations of compact holomorphic Poisson submanifolds which extend Kodaira's series of papers on semi-regularity (deformations of compact complex submanifolds of codimension 1), deformations of compact complex submanifolds of arbitrary codimensions, and stability of compact complex submanifolds in the context of holomorphic Poisson deformations. We also study simultaneous deformations of holomorphic Poisson structures and holomorphic Poisson submanifolds on a fixed underlying compact complex manifold. In appendices, we present deformations of Poisson closed subschemes in the language of functors of Artin rings which is the algebraic version of deformations of holomorphic Poisson submanifolds. We identify first-order deformations and obstructions.

math.AG↗
arXiv2015

Deformations of nonsingular Poisson varieties and Poisson invertible sheaves

In this paper, we study deformations of nonsingular Poisson varieties, deformations of Poisson invertible sheaves and simultaneous deformations of nonsingular Poisson varieties and Poisson invertible sheaves, which extend flat deformation theory of nonsingular varieties and invertible sheaves. In an appendix, we study deformations of Poisson vector bundles. We identify first-order deformations and obstructions.

math.AG↗