Deformations of Holomorphic p-Contact Structures
Abstract
We investigate the notion of holomorphic p-contact structure, that we introduced recently in the scalar case with H. Kasuya and L. Ugarte and in the line-bundle case with K. Broder, in the context of a holomorphic family of compact complex manifolds equipped with a holomorphic family of holomorphic line bundles. Firstly, we show that the existence of a holomorphic p-contact structure is {\bf deformation-open} when a non-jumping assumption is made on the ∂̅-cohomology of bidegree (p, 0). This ought to become a source of further examples of holomorphic p-contact manifolds. Secondly, we obtain a Berndtsson-type {\bf (semi-)positivity} result for the holomorphic vector bundle over the base induced, as a direct image, by the line bundle on the total space that supports the p-contact structures. Thirdly, we introduce a moduli space of relative holomorphic p-contact structures and we show that it is {\bf Hausdorff} and {\bf open} in a certain quotient topological space.
Related
- The Kuranishi space of joint deformations of Calabi--Yau manifolds and holomorphic vector bundles
- Holomorphic isomonodromic deformations of Higgs bundles: absolute lifting, spectral flatness, and nilpotent rigidity
- On deformations of foliated complex analytic structures II: Functors of Artin rings
- Rigidity and Affine Deformations of Foliations on Nilpotent and Solvable Contact Lie Algebras
- Invariant complex structures on the Euclidean motion group as deformations of Calabi-Eckmann structures
BibTeX
@misc{popovici2026deformations,
title = {{Deformations of Holomorphic $p$-Contact Structures}},
author = {Dan Popovici},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20430},
eprint = {2610.20430},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20430},
}
RIS
TY - UNPB
TI - Deformations of Holomorphic p-Contact Structures
AU - Dan Popovici
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20430
UR - https://arxiv.org/abs/2610.20430
AB - We investigate the notion of holomorphic p-contact structure, that we introduced recently in the scalar case with H. Kasuya and L. Ugarte and in the line-bundle case with K. Broder, in the context of a holomorphic family of compact complex manifolds equipped with a holomorphic family of holomorphic line bundles. Firstly, we show that the existence of a holomorphic p-contact structure is {\bf deformation-open} when a non-jumping assumption is made on the ∂̅-cohomology of bidegree (p, 0). This ought to become a source of further examples of holomorphic p-contact manifolds. Secondly, we obtain a Berndtsson-type {\bf (semi-)positivity} result for the holomorphic vector bundle over the base induced, as a direct image, by the line bundle on the total space that supports the p-contact structures. Thirdly, we introduce a moduli space of relative holomorphic p-contact structures and we show that it is {\bf Hausdorff} and {\bf open} in a certain quotient topological space.
ER -