TRIANGULATED CHARACTERIZATIONS OF SINGULARITIES

被引:0
|
作者
Lank, Pat [1 ]
Venkatesh, Sridhar [2 ]
机构
[1] Univ Milan, Dipartimento Matemat F Enriques, Via Cesare Saldini 50, I-20133 Milan, Italy
[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA
基金
美国国家科学基金会;
关键词
triangulated categories; Rouquier dimension; derived splinters; rational singularities; Du Bois singularities; GENERATORS; CATEGORIES; DIMENSIONS;
D O I
10.1017/nmj.2025.11
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This work presents a range of triangulated characterizations for important classes of singularities such as derived splinters, rational singularities, and Du Bois singularities. An invariant called "level" in a triangulated category can be used to measure the failure of a variety to have a prescribed singularity type. We provide explicit computations of this invariant for reduced Nagata schemes of Krull dimension one and for affine cones over smooth projective hypersurfaces. Furthermore, these computations are utilized to produce upper bounds for Rouquier dimension on the respective bounded derived categories.
引用
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页数:15
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