Effective finiteness theorems for maps between canonically polarized compact complex manifolds

Abstract

Effective bounds for the finite number of surjective holomorphic maps between canonically polarized compact complex manifolds of any dimension with fixed domain are proven. Both the case of a fixed target and the case of varying targets are treated. In the case of varying targets, bounds on the complexity of Chow varieties are used.

10 pages

References in corpus (1)

• Bound of automorphisms of projective varieties of general type

Cited by in corpus (4)

• Uniformly effective boundedness of Shafarevich Conjecture-type for families of canonically polarized manifolds
• A bound on the number of curves of a given degree through a general point of a projective variety
• Uniformly effective Shafarevich Conjecture on families of hyperbolic curves over a curve with prescribed degeneracy locus
• On the finiteness theorem for rational maps on a variety of general type