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
收藏
页数:15
相关论文
共 50 条
  • [31] Flooding triangulated terrain
    Liu, YX
    Snoeyink, J
    DEVELOPMENTS IN SPATIAL DATA HANDLING, 2005, : 137 - 148
  • [32] Dimensions of triangulated categories
    Rouquier, Raphael
    JOURNAL OF K-THEORY, 2008, 1 (02) : 193 - 256
  • [33] Stereotomography in triangulated models
    Yang, Kai
    Shao, Wei-Dong
    Xing, Feng-Yuan
    Xiong, Kai
    GEOPHYSICAL JOURNAL INTERNATIONAL, 2018, 214 (02) : 1018 - 1040
  • [34] On deformations of triangulated models
    De Deken, Olivier
    Lowen, Wendy
    ADVANCES IN MATHEMATICS, 2013, 243 : 330 - 374
  • [35] MANY TRIANGULATED SPHERES
    KALAI, G
    DISCRETE & COMPUTATIONAL GEOMETRY, 1988, 3 (01) : 1 - 14
  • [36] ENHANCED TRIANGULATED CATEGORIES
    BONDAL, AI
    KAPRANOV, MM
    MATHEMATICS OF THE USSR-SBORNIK, 1991, 70 (01): : 93 - 107
  • [37] CENTERS OF TRIANGULATED GRAPHS
    CHEPOI, VD
    MATHEMATICAL NOTES, 1988, 43 (1-2) : 82 - 86
  • [39] Karoubianness of a triangulated category
    Le, Jue
    Chen, Xiao-Wu
    JOURNAL OF ALGEBRA, 2007, 310 (01) : 452 - 457
  • [40] On stacked triangulated manifolds
    Datta, Basudeb
    Murai, Satoshi
    ELECTRONIC JOURNAL OF COMBINATORICS, 2017, 24 (04):