论文标题
固有稳定器还原和广义唐纳森 - 托马斯不变
Intrinsic Stabilizer Reduction and Generalized Donaldson-Thomas Invariants
论文作者
论文摘要
令$σ$成为有限的派生类别的稳定条件$ d^b（{\ Mathop {\ rm coh} \ nolimits} w）$的calabi-yau三倍$ w $和$ \ m natercal {m} $ a moduli stack参数$σ$σ$ - semsemistable对象类型。我们定义了广义的Donaldson-Thomas不变式，这些thomas不变性在$ \ Mathcal {M} $中的虚拟计数，充分概括了Kiem，Li和作者在可分离带状支线的情况下引入的方法。 我们构建了一个相关的deligne-mumford stack $ \ wideTilde {\ Mathcal {m}}^{\ Mathbb {c}^\ ast} $，称为$ \ mathbb {c}^\ ast ast $ rigidified intinsic intinsic intinsic intimic ntercal nirt and and and and and and and and and ander nirt and ant ant and and iND iNDERT a nirt and尺寸为零，并通过Kirwan爆炸定义了广义的Donaldson-Thomas不变的程度为相关的虚拟周期$ [\ widetilde {\ Mathcal {\ Mathcal {M}}}^{\ Mathbb {C}^\ ast}^\ ast}] （\ widetilde {\ mathcal {m}}}^{\ Mathbb {c}^\ ast}）$。在$ W $的复杂结构的变形下，这保持不变。应用的示例包括Bridgeland稳定性，多项式稳定性，Gieseker和坡度稳定性。
Let $σ$ be a stability condition on the bounded derived category $D^b({\mathop{\rm Coh}\nolimits} W)$ of a Calabi-Yau threefold $W$ and $\mathcal{M}$ a moduli stack parametrizing $σ$-semistable objects of fixed topological type. We define generalized Donaldson-Thomas invariants which act as virtual counts of objects in $\mathcal{M}$, fully generalizing the approach introduced by Kiem, Li and the author in the case of semistable sheaves. We construct an associated proper Deligne-Mumford stack $\widetilde{\mathcal{M}}^{\mathbb{C}^\ast}$, called the $\mathbb{C}^\ast$-rigidified intrinsic stabilizer reduction of $\mathcal{M}$, with an induced semi-perfect obstruction theory of virtual dimension zero, and define the generalized Donaldson-Thomas invariant via Kirwan blowups to be the degree of the associated virtual cycle $[\widetilde{\mathcal{M}}^{\mathbb{C}^\ast}]^{\mathrm{vir}} \in A_0 (\widetilde{\mathcal{M}}^{\mathbb{C}^\ast})$. This stays invariant under deformations of the complex structure of $W$. Examples of applications include Bridgeland stability, polynomial stability, Gieseker and slope stability.
