Families of affine planes: the existence of a cylinder

TL;DR

This paper proves that a family of complex affine planes is trivial over a Zariski open subset, using a relative contraction theorem, contributing to the understanding of affine plane families in algebraic geometry.

Contribution

It introduces a relative contraction theorem to demonstrate the triviality of affine plane families over a Zariski open subset.

Findings

Family of affine planes is trivial over a Zariski open subset.

Relies on a new relative contraction theorem.

Advances understanding of affine plane families.

Abstract

Given a family of complex affine planes, we show that it is trivial over a Zariski open subset of the base. The proof relies upon a relative version of the contraction theorem.