All abelian quotient C. I.-singularities admit projective crepant resolutions in all dimensions
All abelian quotient C. I.-singularities admit projective crepant resolutions in all dimensions
复制标题
所有阿贝尔商 C. I. 奇点都承认所有维度上的射影绉纹分辨率
DOI：
--
复制
发表时间：
1997
期刊：
影响因子：
--
通讯作者：
G. M. Ziegler
中科院分区：
文献类型：
--
作者：
D. Dais;M. Henk;G. M. Ziegler
对Gorenstein商空间C d/G，直接推广维数d = 4的经典McKay对应首先要求存在射影的、可crepant的去奇异化。由于这原来并不总是可能的，里德问特殊类的商空间，将满足上述财产。我们证明了所有Gorenstein阿贝尔商奇点的基础空间，这是嵌入作为仿射空间中的超曲面的完全交叉，有环面等变的投影crepant决议在所有维度。我们使用复曲面和离散几何的技术。
Abstract For Gorenstein quotient spaces C d/G, a direct generalization of the classical McKay correspondence in dimensionsd⩾4 would primarily demand the existence of projective, crepant desingularizations. Since this turned out to be not always possible, Reid asked about special classes of such quotient spaces that would satisfy the above property. We prove that the underlying spaces of all Gorenstein abelian quotient singularities, which are embeddable as complete intersections of hypersurfaces in an affine space, have torus-equivariant projective crepant resolutions in all dimensions. We use techniques from toric and discrete geometry.