An integral version of Zariski decompositions on normal surfaces

Makoto Enokizono

Published 2020-07-13Version 1

We show that any pseudo-effective divisor on a normal surface decomposes uniquely into its "integral positive" part and "integral negative" part, which is an integral analog of Zariski decompositions. As an application, we give a generalization of the Kawamata-Viehweg vanishing, Ramanujam's 1-connected vanishing and Miyaoka's vanishing theorems on surfaces. By using this vanishing result, we give a simple proof of Reider-type theorems including the log surface case and the relative case.