Curve counting via stable objects in derived cate- gories of Calabi-Yau 4-folds
Curve counting via stable objects in derived cate- gories of Calabi-Yau 4-folds
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通过 Calabi-Yau 4 倍派生类别中的稳定对象进行曲线计数
DOI：
10.1016/j.aim.2022.108531
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发表时间：
2022
影响因子：
1.7
通讯作者：
Yalong Cao and Yukinobu Toda
中科院分区：
文献类型：
--
作者：
ATOBE Hiraku;CHIDA Masataka;IBUKIYAMA Tomoyoshi;KATSURADA Hidenori;YAMAUCHI Takuya;Yalong Cao and Yukinobu Toda
在我们与Maulik的前一篇论文中，我们提出了Calabi-Yau（CY）4-folds上稳定对不变量生成列的一个几何Gopakumar-Vafa（GV）型公式。本文的目的是在导出的范畴中用穿壁现象对上述GV型公式给出一个解释。我们引入不变量计数LePotier的稳定对CY 4倍，并表明，他们计数某些稳定的对象在D 0-D2-D8的束缚态中的衍生类别。我们提出了一个自然的跨壁公式的生成系列我们的不变量，恢复自然GV型公式。例子计算紧凑和复曲面的情况下，以支持我们的猜想。
In our previous paper with Maulik, we proposed a conjectural Gopakumar-Vafa (GV) type formula for the generating series of stable pair invariants on Calabi-Yau (CY) 4-folds. The purpose of this paper is to give an interpretation of the above GV type formula in terms of wall-crossing phenomena in the derived category. We introduce invariants counting LePotier's stable pairs on CY 4-folds, and show that they count certain stable objects in D0-D2-D8 bound states in the derived category. We propose a conjectural wall-crossing formula for the generating series of our invariants, which recovers the conjectural GV type formula. Examples are computed for both compact and toric cases to support our conjecture.