# Algebraic Hyperbolicity for Surfaces in Toric Threefolds

## TL;DR

This paper establishes lower bounds on the genera of curves in very general surfaces within Gorenstein toric threefolds, advancing understanding of algebraic hyperbolicity in these geometric contexts.

## Contribution

It adapts focal loci techniques to derive genus bounds, providing new insights into the algebraic hyperbolicity of surfaces in toric threefolds.

## Key findings

- Lower bounds on genera of curves in general surfaces
- Results on algebraic hyperbolicity of surfaces in toric threefolds
- Application of focal loci techniques in this setting

## Abstract

Adapting focal loci techniques used by Chiantini and Lopez, we provide lower bounds on the genera of curves contained in very general surfaces in Gorenstein toric threefolds. We illustrate the utility of these bounds by obtaining results on algebraic hyperbolicity of very general surfaces in toric threefolds.