# A non-commutative Bertini theorem

## TL;DR

This paper extends the classical Bertini theorem to non-commutative resolutions of singular varieties, providing a new perspective on generic smoothness in non-commutative geometry.

## Contribution

It introduces a non-commutative version of the Bertini theorem, generalizing the classical result to non-commutative resolutions.

## Key findings

- Proves a non-commutative generic smoothness theorem.
- Establishes a non-commutative Bertini theorem.
- Bridges classical algebraic geometry with non-commutative geometry.

## Abstract

We prove a version of the classical 'generic smoothness' theorem with smooth varieties replaced by non-commutative resolutions of singular varieties. This in particular implies a non-commutative version of the Bertini theorem.