Holomorphic self-maps of singular projective curves

Abstract

Here we classify all complex singular irreducibile projective curves. X , such that there exists a holomorphic map f : X → X with f locally biholomorphic at each point of X_{reg} and with deg( f ) ≥ 2 : X is rational and either it has a unique singular point with two branches or it has exactly two singular points, both unibranch.