On the cut\,-\,and\,-\,paste property of algebraic varieties

TL;DR

This paper investigates a specific property of algebraic varieties related to cut-and-paste operations and demonstrates that it does not hold universally, challenging previous assumptions in the field.

Contribution

The paper provides a counterexample showing that the cut-and-paste property does not always apply to algebraic varieties, clarifying limitations of this property.

Findings

The cut-and-paste property fails in general for algebraic varieties.

Counterexamples demonstrate the non-universality of the property.

Results refine understanding of algebraic variety invariants.

Abstract

We show that the above\,-\,named property (after M.\,Larsen and V.\,Lunts) does not hold in general.