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On deformations of foliated complex analytic structures I: Theorems of existence and completeness

  • Chunghoon Kim
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Abstract

We study deformations of foliated complex analytic structures defined by locally free subsheaves of tangent sheaves and locally free subsheaves of cotangent sheaves on the basis of Kodaira-Spencer's deformation theory. We prove theorems of existence and completeness for deformations of foliated complex analytic structures defined by locally free subsheaves of tangent sheaves as analogues of theorems of existence and completeness for deformations of complex analytic structures by Kodaira-Spencer. We prove theorems of existence and completeness for deformations of foliated complex analytic structures defined by locally free subsheaves of cotangent sheaves. We also prove theorems of existence and completeness for simultaneous deformations when singular holomorphic foliations on compact complex manifolds are defined by locally free subsheaves of tangent and cotangent sheaves at the same time.

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Cite

BibTeXRIS
BibTeX
@misc{kim2026deformations,
  title = {{On deformations of foliated complex analytic structures I: Theorems of existence and completeness}},
  author = {Chunghoon Kim},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34830},
  eprint = {2609.34830},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34830},
}
RIS
TY  - UNPB
TI  - On deformations of foliated complex analytic structures I: Theorems of existence and completeness
AU  - Chunghoon Kim
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34830
UR  - https://arxiv.org/abs/2609.34830
AB  - We study deformations of foliated complex analytic structures defined by locally free subsheaves of tangent sheaves and locally free subsheaves of cotangent sheaves on the basis of Kodaira-Spencer's deformation theory. We prove theorems of existence and completeness for deformations of foliated complex analytic structures defined by locally free subsheaves of tangent sheaves as analogues of theorems of existence and completeness for deformations of complex analytic structures by Kodaira-Spencer. We prove theorems of existence and completeness for deformations of foliated complex analytic structures defined by locally free subsheaves of cotangent sheaves. We also prove theorems of existence and completeness for simultaneous deformations when singular holomorphic foliations on compact complex manifolds are defined by locally free subsheaves of tangent and cotangent sheaves at the same time.
ER  -