Deformations of an affine Gorenstein toric pair

Filip, Matej (author)

We consider deformations of a pair $(X,\partial X)$, where $X$ is an affine toric Gorenstein variety and $\partial X$ is its boundary. We compute the tangent and obstruction space for the corresponding deformation functor and for an admissible lattice degree $m$ we construct the miniversal deformation of $(X,\partial X)$ in degrees $-km$, for all $k\in{\mathbb N}$. This in particular generalizes Altmann's construction of the miniversal deformation of an isolated Gorenstein toric singularity to an arbitrary non-isolated Gorenstein toric singularity. Moreover, we show that the irreducible components of the reduced miniversal deformation are in one to one correspondence with maximal Minkowski decompositions of the polytope $P\cap(m=1)$, where $P$ is the lattice polytope defining $X$.

• Language: English
• Keywords: deformation theory, toric singularities
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FE - Faculty of Electrical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: Str. 419-445
• Numbering: Vol. 687
• PID: 20.500.12556/RUL-182677
• UDC: 512
• ISSN on article: 0021-8693
• DOI: 10.1016/j.jalgebra.2025.09.007
• COBISS.SI-ID: 250487811
• Publication date in RUL: 20.05.2026

Record is a part of a journal

• Title: Journal of algebra
• Shortened title: J. algebra
• Publisher: Elsevier
• ISSN: 0021-8693
• COBISS.SI-ID: 1310986

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0222
• Name: Algebra, teorija operatorjev in finančna matematika

• Funder: ARRS - Slovenian Research Agency
• Project number: J1-60011
• Name: Prirezani momentni problem prek realne algebraične geometrije