Divisors on surfaces isogenous to a product of mixed type with $p_g=0$

TL;DR

This paper investigates the geometric cones of certain algebraic surfaces called surfaces isogenous to a product of mixed type with geometric genus zero, establishing that all reducible fake quadrics are Mori dream surfaces.

Contribution

It proves that all reducible fake quadrics are Mori dream surfaces, advancing understanding of their geometric and algebraic properties.

Findings

Effective, nef, and semiample cones characterized for these surfaces.

All reducible fake quadrics are Mori dream surfaces.

Provides new insights into the structure of surfaces with $p_g=0$.

Abstract

In this paper, we study effective, nef and semiample cones of surfaces isogenous to a product of mixed type with $p_g=0$. In particular, we prove that all reducible fake quadrics are Mori dream surfaces.