# On del Pezzo fibrations in positive characteristic

## TL;DR

This paper investigates properties of three-dimensional del Pezzo fibrations over fields of positive characteristic, providing bounds on torsion indices and constructing inseparable sections, with a focus on log del Pezzo surfaces over imperfect fields.

## Contribution

It introduces explicit bounds for torsion line bundles and constructs inseparable sections in del Pezzo fibrations in positive characteristic, advancing understanding of their structure.

## Key findings

- Bound for torsion index of line bundles established
- Existence of purely inseparable sections with bounded degree shown
- Analysis of log del Pezzo surfaces over imperfect fields conducted

## Abstract

We establish two results on three-dimensional del Pezzo fibrations in positive characteristic. First, we give an explicit bound for torsion index of relatively torsion line bundles. Second, we show the existence of purely inseparable sections with explicit bounded degree. To prove these results, we study log del Pezzo surfaces defined over imperfect fields.