Examples of Mori dream surfaces of general type with p g = 0

Abstract

In this paper we study effective, nef and semiample cones of minimal surfaces of general type with p g =0. We provide examples of minimal surfaces of general type with p g =0 and 2≤K 2 ≤9 which are Mori dream spaces. On these examples we also give explicit description of their effective cones with all negative curves. We also present non-minimal surfaces of general type with p g =0 that are not Mori dream surfaces. © 2019 Elsevier Inc. All rights reserved.