On the boundedness of the denominators in the Zariski decomposition on surfaces

Abstract

AbstractZariski decompositions play an important role in the theory of algebraic surfaces. For making geometric use of the decomposition of a given divisor, one needs to pass to a multiple of the divisor in order to clear denominators. It is therefore an intriguing question whether the surface has a “universal denominator” that can be used to simultaneously clear denominators in all Zariski decompositions on the surface. We prove in this paper that, somewhat surprisingly, this condition of