Log Fano varieties over function fields of curves

TL;DR

This paper proves that for certain log Fano varieties over function fields of curves, the integral points are Zariski dense outside a finite set, under specific boundary conditions.

Contribution

It establishes the density of integral points on log Fano varieties over function fields with boundary having positive normal bundle, providing new insights into their arithmetic geometry.

Findings

Integral points are Zariski dense after removing finitely many points.

The boundary's positive normal bundle condition is crucial for density.

Results apply to smooth log Fano varieties over function fields.

Abstract

Consider a smooth log Fano variety over the function field of a curve. Suppose that the boundary has positive normal bundle. Choose an integral model over the curve. Then integral points are Zariski dense, after removing an explicit finite set of points on the base curve.