Hall algebras in the derived category and higher-rank DT invariants

被引:12
作者
Toda, Yukinobu [1 ]
机构
[1] Univ Tokyo, Kavli Inst Phys & Math Universe WPI, 5-1-5 Kashiwanoha, Kashiwa, Chiba 2778583, Japan
来源
ALGEBRAIC GEOMETRY | 2020年 / 7卷 / 03期
关键词
Donaldson- Thomas invariants; Hall algebras; derived category; BRIDGELAND STABILITY CONDITIONS; ABELIAN CATEGORIES; HILBERT SCHEMES; STABLE OBJECTS; CONFIGURATIONS; THREEFOLDS; THEOREM; MODULI;
D O I
10.14231/AG-2020-008
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We remark that the combination of the works of Ben-Bassat-Brav-Bussi-Joyce and Alper-Hall-Rydh imply the conjectured local description of the moduli stacks of semiSchur objects in the derived category of coherent sheaves on projective Calabi-Yau 3-folds. This result was assumed in the author's previous papers to apply wall-crossing formulas of DT-type invariants in the derived category, for example DT/PT correspondence, rationality, etc. We also show that the above result can be applied to prove the higher-rank version of the DT/PT correspondence and rationality.
引用
收藏
页码:240 / 262
页数:23
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