On rigidity of factorial trinomial hypersurfaces

TL;DR

This paper characterizes the rigidity of factorial trinomial hypersurfaces, showing they are rigid precisely when all exponents are at least 2, advancing understanding of their algebraic structure.

Contribution

It provides a complete criterion for the rigidity of factorial trinomial hypersurfaces based on the exponents in the defining trinomial.

Findings

Factorial trinomial hypersurfaces are rigid iff all exponents are ≥ 2.

The paper establishes a necessary and sufficient condition for rigidity.

It deepens the understanding of the algebraic properties of trinomial hypersurfaces.

Abstract

An affine algebraic variety $X$ is rigid if the algebra of regular functions ${\mathbb K}[X]$ admits no nonzero locally nilpotent derivation. We prove that a factorial trinomial hypersurface is rigid if and only if every exponent in the trinomial is at least 2.