English

On Rigidity and the Albanese Variety for Parallelizable Manifolds

Algebraic Geometry 2016-09-07 v1

Abstract

We study the rigidity questions and the Albanese Variety for Complex Parallelizable Manifolds. Both are related to the study of the cohomology group H1(X,O)H^1(X,\mathcal O). In particular we show that a compact complex parallelizable manifold is rigid iff b1(X)=0b_1(X)=0 iff Alb(X)={e}(X)=\{e\} iff H1(X,O)=0H^1(X,\mathcal O)=0.

Keywords

Cite

@article{arxiv.math/9705215,
  title  = {On Rigidity and the Albanese Variety for Parallelizable Manifolds},
  author = {Jörg Winkelmann},
  journal= {arXiv preprint arXiv:math/9705215},
  year   = {2016}
}
R2 v1 2026-07-22T17:56:47.906Z