论文标题
复曲面戈伦斯坦对的变形
Deformations of a toric Gorenstein pair
论文作者
论文摘要
我们考虑了一对$（x，\ partial x）$的变形，其中$ x $是一种仿射的gorenstein品种，$ \ partial x $是其边界。我们计算相应变形函数的切线和阻塞空间以及可允许的晶格学位$ m $我们以$（x，\ partial x）$ $ -km $ $ -km $的微型变形，用于所有$ k \ in \ mathbb {n} $。这尤其概括了阿尔特曼（Altmann）构造孤立的戈伦斯坦（Gorenstein）曲折奇异性的微型变形，以实现任意的非分离的戈伦斯坦（Gorenstein）曲折奇异性。我们看到，处理一对$（x，\ partial x）$的变形，而不仅仅是$ x $的变形更为自然，因为许多计算实际上更容易。
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 $k\in \mathbb{N}$ together. 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. We see that it is more natural to work with deformations of a pair $(X,\partial X)$ rather than only with deformations of $X$, since many computations are in fact easier.
