Deformations of elliptic fibre bundles in positive characteristic

TL;DR

This paper investigates the deformation theory of elliptic fibre bundles over curves in positive characteristic, providing examples of non-liftable elliptic surfaces, linking liftability to a conjecture on automorphisms, and classifying deformations of bielliptic surfaces.

Contribution

It introduces new examples of non-liftable elliptic surfaces, connects liftability to a conjecture of F. Oort, and classifies deformations of bielliptic surfaces in positive characteristic.

Findings

Examples of non-liftable elliptic surfaces in characteristics two and three.

Liftability of certain elliptic fibrations linked to Oort's conjecture.

Complete classification of deformations of bielliptic surfaces.

Abstract

We study deformation theory of elliptic fibre bundles over curves in positive characteristics. As applications, we give examples of non-liftable elliptic surfaces in charactertic two and three, which answers a question of Katsura and Ueno. Also, we construct a class of elliptic fibrations, whose liftability is equivalent to a conjecture of F. Oort concerning the liftability of automorphisms of curves. Finally, we classify deformations of bielliptic surfaces.