A criterion for a degree-one holomorphic map to be a biholomorphism. Issue 7 (3rd July 2017)

• Record Type: Journal Article
• Authors: Bharali, Gautam; Biswas, Indranil; Schumacher, Georg
• Is Part Of: Complex variables and elliptic equations. Volume 62:Issue 7(2017)
• Page Start: 914
• Page End: 918
• Publication Date: 2017-07-03
• Subjects: Bimeromorphic maps -- degree-one maps; 32H02 -- 32J18; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2016.1252342
• Languages: English
• ISSNs: 1747-6933

Abstract

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.