ON STRONG EXCEPTIONAL COLLECTIONS OF LINE BUNDLES OF MAXIMAL LENGTH ON FANO TORIC DELIGNE-MUMFORD STACKS

被引：0

作者：

Borisov, Lev ^{[1
]}

Wang, Chengxi ^{[1
]}

机构：

[1] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

来源：

ASIAN JOURNAL OF MATHEMATICS | 2021年 / 25卷 / 04期

关键词：

toric Deligne-Mumford stacks; Picard groups; strong exceptional collections; line bundles; derived categories;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study strong exceptional collections of line bundles on Patio toric Deligne-Mumford stacks P-Sigma with rank of Picard group at most two. We prove that any strong exceptional collection of line bundles generates the derived category of P-Sigma, as long as the number of elements in the collection equals the rank of the (Grothendieck) K-theory group of P-Sigma.

引用

页码：505 / 520

页数：16

共 22 条

[1] Smooth toric Deligne-Mumford stacks
Fantechi, Barbara
Mann, Etienne
Nironi, Fabio
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2010, 648 : 201 - 244
[2] A NOTE ON TORIC DELIGNE-MUMFORD STACKS
Perroni, Fabio
[J]. TOHOKU MATHEMATICAL JOURNAL, 2008, 60 (03) : 441 - 458
[3] GLOBAL QUOTIENTS AMONG TORIC DELIGNE-MUMFORD STACKS
Harada, Megumi
Krepski, Derek
[J]. OSAKA JOURNAL OF MATHEMATICS, 2015, 52 (01) : 237 - 269
[4] The orbifold Chow ring of toric Deligne-Mumford stacks
Borisov, LA
Chen, L
Smith, GG
[J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 18 (01) : 193 - 215
[5] On the conjecture of King for smooth toric Deligne-Mumford stacks
Borisov, Lev
Hua, Zheng
[J]. ADVANCES IN MATHEMATICS, 2009, 221 (01) : 277 - 301
[6] Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks
Iritani, Hiroshi
[J]. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2020, 16
[7] The integral (orbifold) Chow ring of toric Deligne-Mumford stacks
Jiang, Yunfeng
Tseng, Hsian-Hua
[J]. MATHEMATISCHE ZEITSCHRIFT, 2010, 264 (01) : 225 - 248
[8] The Coherent-Constructible Correspondence for Toric Deligne-Mumford Stacks
Fang, Bohan
Liu, Chiu-Chu Melissa
Treumann, David
Zaslow, Eric
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2014, 2014 (04) : 914 - 954
[9] K-Theoretic and Categorical Properties of Toric Deligne-Mumford Stacks
Coates, Tom
Iritani, Hiroshi
Jiang, Yunfeng
Segal, Ed
[J]. PURE AND APPLIED MATHEMATICS QUARTERLY, 2015, 11 (02) : 239 - 266
[10] A note on finite abelian gerbes over toric Deligne-Mumford stacks
Jiang, Yunfeng
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (12) : 4151 - 4156

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