Surfaces with surjective endomorphisms of any given degree (Q658949)

Let \(X\) be a complex projective variety. A surjective endomorphism \(f:X\to X\) is said to be a nontrivial self-map if it has degree strictly greater than 1. In the paper under review the authors study nontrivial self-maps of surfaces. The main result of the paper is Theorem 2 where a complete classification of complex projective surfaces admitting self-maps of any given degree is provided. An explicit construction of some surfaces satisfying this property is given in Example 21 thus showing that the given classification does not contain empty items. The main tools in the proof of Theorem 2 are Theorem 3.2 in [\textit{Y. Fujimoto}, Publ. Res. Inst. Math. Sci. 38, No. 1, 33--92 (2002; Zbl 1053.14049)] and Theorem 3 in [\textit{N. Nakayama}, Kyushu J. Math. 56, No. 2, 433--446 (2002; Zbl 1049.14029)] where a complete description of complex projective surfaces admitting \textit{at least} a nontrivial self-map is provided.