Q-factorial Laurent rings

TL;DR

This paper investigates conditions under which rings associated with Laurent polynomials are Q-factorial, extending known results from higher dimensions to the three-variable case.

Contribution

It provides a sufficient condition for the Q-factoriality of rings linked to very general Laurent polynomials in three variables.

Findings

Established a criterion for Q-factoriality in three-variable Laurent rings.

Extended factoriality results from higher dimensions to three variables.

Contributed to the understanding of algebraic properties of Laurent rings.

Abstract

Dolgachev proved that, for any field k, the ring naturally associated to a generic Laurent polynomial in d variables, $d \geq 4$, is factorial. We prove a sufficient condition for the ring associated to a very general complex Laurent polynomial in d=3 variables to be Q-factorial.