Work

Deformations of an affine Gorenstein toric pair

Year: 2025

Type: article

Abstract: We consider deformations of a pair ( X , ∂ X ) , where X is an affine toric Gorenstein variety and ∂ 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 , ∂ X ) in degrees − k m , for all k ∈ 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 ∩ ( m = 1 ) , where P is the lattice polytope defining X .

Source: Journal of Algebra

DOI: 10.1016/j.jalgebra.2025.09.007

Author: Matej Filip

Institutions: University of Ljubljana, Institute of Mathematics, Physics, and Mechanics

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,310

Funder: Javna Agencija za Raziskovalno Dejavnost RS