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arXiv · 1610.06286

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

Gautam Bharali·Indranil Biswas·Georg Schumacher
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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.

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Gautam Bharali, Indranil Biswas, Georg Schumacher. 2016-10-20. A criterion for a degree-one holomorphic map to be a biholomorphism. https://arxiv.org/abs/1610.06286

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