Bertini theorems admitting base changes

TL;DR

This paper extends Bertini theorems to algebraic varieties over excellent rings, showing that certain singularities remain stable under base changes and enlargements.

Contribution

It generalizes classical Bertini theorems from fields to excellent rings, providing new stability results for singularities under base changes.

Findings

Singularities are stable under base changes over excellent rings.

Analogous Bertini theorems hold in the context of excellent rings.

Results apply to a broad class of algebraic varieties and linear systems.

Abstract

Given a base point free linear system on an algebraic variety, many classes of singularities are stable under taking suitable members after enlarging the base field. We establish analogous results when the base ring is an excellent ring.