Laurent polynomials and deformations of non-isolated Gorenstein toric singularities

Filip, Matej (avtor)

We 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.

• Jezik: Angleški jezik
• Ključne besede: deformation theory, toric singularities, Laurent polynomials, mirror symmetry, Fano manifolds
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FE - Fakulteta za elektrotehniko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2026
• Št. strani: 56 str.
• Številčenje: Vol. 487, art. 110775
• PID: 20.500.12556/RUL-182861
• UDK: 514.7
• ISSN pri članku: 0001-8708
• DOI: 10.1016/j.aim.2025.110775
• COBISS.SI-ID: 267113219
• Datum objave v RUL: 26.05.2026

Gradivo je del revije

• Naslov: Advances in mathematics
• Skrajšan naslov: Adv. math.
• Založnik: Elsevier
• ISSN: 0001-8708
• COBISS.SI-ID: 24891904

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.