@article{715d6f4215ce47a9884ae388af6c5058,

title = "Algebraically hyperbolic manifolds have finite automorphism groups",

abstract = "A projective manifold M is algebraically hyperbolic if there exists a positive constant A such that the degree of any curve of genus g on M is bounded from above by A(g-1). A classical result is that Kobayashi hyperbolicity implies algebraic hyperbolicity. It is known that Kobayashi hyperbolic manifolds have finite automorphism groups. Here, we prove that, more generally, algebraically hyperbolic projective manifolds have finite automorphism groups.",

keywords = "Albanese map, Algebraic hyperbolicity, Kobayashi hyperbolicity, group of automorphisms",

author = "Bogomolov, {Fedor A.} and Ljudmila Kamenova and Misha Verbitsky",

note = "Funding Information: Most of the results in this paper were finalized during the Komplexe Analysis Ober-wolfach Workshop in 2017. The second and third-named authors are grateful to the Oberwolfach organizers and staff for their hospitality. The first-named author has been funded by the Russian Academic Excellence Project “5-100” and acknowledges support by Simons travel grant and by the EPSRC program grant EP/M024830. We are thankful to the referee for many valuable comments and corrections to the earlier version. Funding Information: The second author is partially supported by a grant from the Simons Foundation/SFARI (522730, LK) and the third author is partially supported by the Russian Academic Excellence Project “5-100”, CNPq Process 313608/2017-2 and FAPERJ E-26/202.912/2018. Publisher Copyright: {\textcopyright} 2020 World Scientific Publishing Company.",

year = "2020",

month = mar,

day = "1",

doi = "10.1142/S0219199719500032",

language = "English (US)",

volume = "22",

journal = "Communications in Contemporary Mathematics",

issn = "0219-1997",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "2",

}