Examples of Mori dream surfaces of general type with $p_g=0$

TL;DR

This paper explores specific minimal surfaces of general type with geometric genus zero, providing examples of Mori dream spaces and detailed descriptions of their cones and curves, while also discussing non-Mori dream cases.

Contribution

It presents explicit examples of Mori dream surfaces with various invariants and describes their effective cones and negative curves in detail.

Findings

Examples of Mori dream surfaces with 2 ≤ K^2 ≤ 9 and p_g=0.

Explicit descriptions of effective cones and negative curves.

Identification of non-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 $p_g=0, 2 \leq K^2 \leq 9$ which are Mori dream spaces. On these examples we also give explicit description of effective cones and all irreducible reduced curves of negative self-intersection. We also present non-minimal surfaces of general type with $p_g=0$ that are not Mori dream surfaces.