Laurent polynomials and deformations of non-isolated Gorenstein toric singularitiesFilip, Matej (Avtor) deformation theorytoric singularitiesLaurent polynomialsmirror symmetryFano manifoldsWe establish a correspondence between one-parameter deformations of an affine Gorenstein toric pair $(X_P, \partial X_P)$, defined by a polytope $P$, and mutations of a Laurent polynomial $f$ with Newton polytope $\Delta(f) = P$. For a Laurent polynomial $f$ in two variables, we construct a formal deformation of the three-dimensional Gorenstein toric pair $(X_{\Delta(f)}, \partial X_{\Delta(f)})$ over ${\mathbb C}[[{\mathbf T}_f]]$, where ${\mathbf T}_f$ is the set of deformation parameters arising from mutations. The general fibre of this deformation is smooth if and only if $f$ is $0$-mutable. The Kodaira-Spencer map of the constructed deformation is injective, and if $f$ is maximally mutable, then the deformation cannot be nontrivially extended to a larger smooth base space.20262026-05-26 09:38:50Članek v reviji182861sl