On deformations of foliated complex analytic structures I: Theorems of existence and completeness
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Kim, Chunghoon
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214701166