Deformation families of open Calabi-Yau manifolds and Steinness

Abstract

This paper is to construct deformation families of open Calabi-Yau manifolds together with some discussions on Steinness. Firstly, we construct a nontrivial compactifiable deformation of open Calabi-Yau manifolds from rational elliptic surface with global sections. Secondly, we give a condition for the existence of an elliptic fibration with global sections on the complex analytic family of rational elliptic surface with global sections, construct a holomorphic involution on the compactifiable deformation family and claim the non-Steinness for all the compactifiable deformation families constructed. Finally, we give some discussions on the non-Steinness of the quasi-projective variety from CP²\#9 CP̅² corresponding to a conjecture by Marco Brunella and construct deformation families whose fibers were conjectured to be Stein by Andreas Höring and Thomas Peternel.

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BibTeX RIS

BibTeX

@misc{xu2026deformation,
  title = {{Deformation families of open Calabi-Yau manifolds and Steinness}},
  author = {Fan Xu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10454},
  eprint = {2609.10454},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10454},
}

RIS

TY  - UNPB
TI  - Deformation families of open Calabi-Yau manifolds and Steinness
AU  - Fan Xu
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.10454
UR  - https://arxiv.org/abs/2609.10454
AB  - This paper is to construct deformation families of open Calabi-Yau manifolds together with some discussions on Steinness. Firstly, we construct a nontrivial compactifiable deformation of open Calabi-Yau manifolds from rational elliptic surface with global sections. Secondly, we give a condition for the existence of an elliptic fibration with global sections on the complex analytic family of rational elliptic surface with global sections, construct a holomorphic involution on the compactifiable deformation family and claim the non-Steinness for all the compactifiable deformation families constructed. Finally, we give some discussions on the non-Steinness of the quasi-projective variety from CP^2\#9 CP̅^2 corresponding to a conjecture by Marco Brunella and construct deformation families whose fibers were conjectured to be Stein by Andreas Höring and Thomas Peternel.
ER  -

Abstract

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