A Barth-Type Theorem for Branched Coverings of Projective Space.
We consider polynomial mappings (f,g) of ℂ² with constant nontrivial jacobian. Using the Riemann-Hurwitz relation we prove among other things the following: If g - c (resp. f - c) has at most two branches at infinity for infinitely many numbers c or if f (resp. g) is proper on the level set (resp. ), then (f,g) is bijective.
We obtain sufficient and necessary conditions (in terms of positive singular metrics on an associated line bundle) for a positive divisor D on a projective algebraic variety X to be attracting for a holomorphic map f:X → X.