论文标题
稳定的当地Calabi-yau的稳定对不变4倍
Stable pair invariants of local Calabi-Yau 4-folds
论文作者
论文摘要
在2008年，Klemm-Pandharipande使用gromov-witten理论定义了calabi-yau 4倍$ x $的gopakumar-vafa类型不变性。最近，Cao-Maulik-Toda在稳定对理论方面提出了对这些不变的猜想描述。当$ x $是表面$ s $上两条线束的总和的总空间，而所有稳定的对均在零部分上在理论上支持方案，我们就$ s $的Hilbert of Soptile方案上的相交数字表示稳定的对不变性。作为应用程序，我们获得了低度曲线类别的CAO-Maulik-TODA猜想的新验证，并找到与Carlsson-Okounkov数字的联系。我们的某些验证涉及最近在Bousseau-Brini-van Garrel的对数本地原理的背景下确定的零gopakumar-Vafa类型不变性。最后，使用顶点形式主义，当增厚曲线贡献时，我们还提供了对Cao-Maulik-toda猜想的更多验证，也为局部$ \ Mathbb {p}^3 $提供了一些验证。
In 2008, Klemm-Pandharipande defined Gopakumar-Vafa type invariants of a Calabi-Yau 4-fold $X$ using Gromov-Witten theory. Recently, Cao-Maulik-Toda proposed a conjectural description of these invariants in terms of stable pair theory. When $X$ is the total space of the sum of two line bundles over a surface $S$, and all stable pairs are scheme theoretically supported on the zero section, we express stable pair invariants in terms of intersection numbers on Hilbert schemes of points on $S$. As an application, we obtain new verifications of the Cao-Maulik-Toda conjectures for low degree curve classes and find connections to Carlsson-Okounkov numbers. Some of our verifications involve genus zero Gopakumar-Vafa type invariants recently determined in the context of the log-local principle by Bousseau-Brini-van Garrel. Finally, using the vertex formalism, we provide a few more verifications of the Cao-Maulik-Toda conjectures when thickened curves contribute and also for the case of local $\mathbb{P}^3$.
