| Title: | Deformations of an affine Gorenstein toric pair |
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| Authors: | ID Filip, Matej (Author) |
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| Files: |  PDF - Presentation file, download (1,04 MB)
MD5: ABACE1BC875B06B20514890BB13D569A
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0021869325005320
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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 $X$. |
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| Keywords: | deformation theory, toric singularities |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.02.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | str. 419-445 |
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| Numbering: | Vol. 687 |
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| PID: | 20.500.12556/DiRROS-23756  |
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| UDC: | 512 |
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| ISSN on article: | 0021-8693 |
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| DOI: | 10.1016/j.jalgebra.2025.09.007 |
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| COBISS.SI-ID: | 250487811 |
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| Note: |
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| Publication date in DiRROS: | 01.10.2025 |
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| Views: | 191 |
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| Downloads: | 70 |
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