On Lang's conjecture for some product-quotient surfaces

TL;DR

This paper proves effective versions of Lang's conjectures for certain complex surfaces of general type, specifically product-quotient surfaces with specific invariants, advancing understanding of their geometric properties.

Contribution

It provides the first effective results confirming Lang's conjectures for a class of surfaces with particular invariants.

Findings

Confirmed algebraic Lang's conjecture for these surfaces.

Validated analytic Lang's conjecture in this context.

Established bounds related to rational points and entire curves.

Abstract

We prove effective versions of algebraic and analytic Lang's conjectures for product-quotient surfaces of general type with $P_g=0$ and $c_1^2=c_2$.