Moduli stacks and invariants of semistable objects on K3 surfaces
Moduli stacks and invariants of semistable objects on K3 surfaces
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DOI：
10.1016/j.aim.2007.11.010
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发表时间：
2007-03
影响因子：
1.7
通讯作者：
Yukinobu Toda
中科院分区：
文献类型：
--
作者：
Yukinobu Toda
对于K ~ 3曲面X及其凝聚层的有界导范畴D（X），我们给出了D（X）在T意义下的稳定性条件的概念。布里奇兰本文证明了D（X）中具有固定数值类和相位的半稳定对象的模栈可以表示为C上的有限型Artin栈。继D. Joyce的工作中，我们引入了D（X）中计数半稳定对象的不变量，并证明了不变量与稳定性条件的选择无关。
For a K3 surface X and its bounded derived category of coherent sheaves D(X), we have the notion of stability conditions on D(X) in the sense of T. Bridgeland. In this paper, we show that the moduli stack of semistable objects in D(X) with a fixed numerical class and a phase is represented by an Artin stack of finite type over C. Then following D. Joyce's work, we introduce the invariants counting semistable objects in D(X), and show that the invariants are independent of a choice of a stability condition.