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Demailly’s notion of algebraic hyperbolicity: geometricity, boundedness, moduli of maps

Demailly’s notion of algebraic hyperbolicity: geometricity, boundedness, moduli of maps

Abstract Demailly’s conjecture, which is a consequence of the Green–Griffiths–Lang conjecture on varieties of general type, states that an algebraically hyperbolic complex projective variety is Kobayashi hyperbolic. Our aim is to provide evidence for Demailly’s conjecture by verifying several predictions it makes. We first define what an algebraically hyperbolic projective …