论文标题
在卡拉比YAU上计数不正当的相干系统4倍
Counting perverse coherent systems on Calabi-Yau 4-folds
论文作者
论文摘要
Nagao-Nakajima引入了在Calabi-Yau的小分辨率3倍的小分辨率上引入了稳定的不正当系统的计数，并在已解决的Conifold上确定了它们。他们的不变性在某些稳定条件的会议室中恢复了DT/PT不变性和Szendröi的非交往不变。在本文中，我们研究了他们在4倍4倍的Calabi-Yau上的工作的类似物。我们使用主要插入来定义稳定的变态相干系统的计数不变性，并在所有稳定条件下计算它们。我们还研究了局部解决的Conifold $ \ Mathcal {O} _ {\ Mathbb {p}^1}（ - 1，-1,0）$不变的计数。我们猜想了它们的墙壁交叉公式，该公式在尺寸还原时恢复了nagao-nakajima在解决方案上的墙壁交叉公式。
Nagao-Nakajima introduced counting invariants of stable perverse coherent systems on small resolutions of Calabi-Yau 3-folds and determined them on the resolved conifold. Their invariants recover DT/PT invariants and Szendröi's non-commutative invariants in some chambers of stability conditions. In this paper, we study an analogue of their work on Calabi-Yau 4-folds. We define counting invariants for stable perverse coherent systems using primary insertions and compute them in all chambers of stability conditions. We also study counting invariants of local resolved conifold $\mathcal{O}_{\mathbb{P}^1}(-1,-1,0)$ defined using torus localization and tautological insertions. We conjecture a wall-crossing formula for them, which upon dimensional reduction recovers Nagao-Nakajima's wall-crossing formula on resolved conifold.
