A criterion for a degree-one holomorphic map to be a biholomorphism

Gautam Bharali; Indranil Biswas; Georg Schumacher

A criterion for a degree-one holomorphic map to be a biholomorphism

Complex Variables 2016-10-21 v1 Algebraic Geometry

Authors: Gautam Bharali , Indranil Biswas , Georg Schumacher

Abstract

Let $X$ and $Y$ be compact connected complex manifolds of the same dimension with $b_2(X)= b_2(Y)$ . We prove that any surjective holomorphic map of degree one from $X$ to $Y$ is a biholomorphism. A version of this was established by the first two authors, but under an extra assumption that $\dim H^1(X {\mathcal O}_X)\,=\,\dim H^1(Y {\mathcal O}_Y)$ . We show that this condition is actually automatically satisfied.

Keywords

holomorphic map biholomorphism compact complex manifolds degree one second betti number sheaf cohomology

Cite

@article{arxiv.1610.06286,
  title  = {A criterion for a degree-one holomorphic map to be a biholomorphism},
  author = {Gautam Bharali and Indranil Biswas and Georg Schumacher},
  journal= {arXiv preprint arXiv:1610.06286},
  year   = {2016}
}

Comments

Complex Variables and Elliptic Equations (to appear)

A criterion for a degree-one holomorphic map to be a biholomorphism

Abstract

Keywords

Cite

Comments

Related papers