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

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.
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