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On deformations of foliated complex analytic structures III: Unfoldings

  • Chunghoon Kim
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Abstract

We study unfoldings of foliated complex analytic structures defined by locally free subsheaves of cotangent sheaves. We prove theorem of existence for unfoldings of foliated complex analytic structures defined by locally free subsheaves of cotangent sheaves for one-parameter families. We prove theorem of completeness for unfoldings of foliated complex analytic structures defined by locally free subsheaves of cotangent sheaves. We also present unfoldings of foliated nonsingular varieties defined by locally free subsheaves of cotangent sheaves in the language of functors of Artin rings which is the algebraic version of unfoldings of foliated complex analytic structures. We identify first-order unfoldings and obstructions.

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Cite

BibTeXRIS
BibTeX
@misc{kim2026deformations,
  title = {{On deformations of foliated complex analytic structures III: Unfoldings}},
  author = {Chunghoon Kim},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20011},
  eprint = {2610.20011},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20011},
}
RIS
TY  - UNPB
TI  - On deformations of foliated complex analytic structures III: Unfoldings
AU  - Chunghoon Kim
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20011
UR  - https://arxiv.org/abs/2610.20011
AB  - We study unfoldings of foliated complex analytic structures defined by locally free subsheaves of cotangent sheaves. We prove theorem of existence for unfoldings of foliated complex analytic structures defined by locally free subsheaves of cotangent sheaves for one-parameter families. We prove theorem of completeness for unfoldings of foliated complex analytic structures defined by locally free subsheaves of cotangent sheaves. We also present unfoldings of foliated nonsingular varieties defined by locally free subsheaves of cotangent sheaves in the language of functors of Artin rings which is the algebraic version of unfoldings of foliated complex analytic structures. We identify first-order unfoldings and obstructions.
ER  -