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

作者：Bharali Gautam; Biswas Indranil^*; Schumacher Georg

来源：Complex Variables and Elliptic Equations, 2017, 62(7): 914-918.

DOI：10.1080/17476933.2016.1252342

• Bimeromorphic maps
• degree-one maps

Let X and Y be compact connected complex manifolds of the same dimension with b2( X) = b2( 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 H1( X, OX) = dim H1( Y, OY). We show that this condition is actually automatically satisfied.

• 出版日期2017