On Rigidity and the Albanese Variety for Parallelizable Manifolds

Details On Rigidity and the Albanese Variety for Parallelizable Manifolds On Rigidity and the Albanese Variety for Parallelizable Manifolds

1997-05-05

arxiv.org/abs/math/9705215v1

Mathematics

Algebraic Geometry

Scientific paper

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

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