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

Abstract

Let X and Y be compact connected complex manifolds of the same dimension with . 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 . We show that this condition is actually automatically satisfied.

Keywords:

• Bimeromorphic maps
• degree-one maps

AMS Subject Classifications:

• 32H02
• 32J18

Acknowledgements

The second-named author thanks the Philipps-Universität, where the work for this paper was carried out, for its hospitality. He is partially supported by a J.C. Bose Fellowship.

Notes

No potential conflict of interest was reported by the authors.