Deformations of an affine Gorenstein toric pair
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2020
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916947759726592 |
|---|---|
| author | Filip, Matej |
| author_facet | Filip, Matej |
| contents | 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 $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_12960 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Deformations of an affine Gorenstein toric pair Filip, Matej Algebraic Geometry 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 $X$. |
| title | Deformations of an affine Gorenstein toric pair |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2006.12960 |