论文标题
gopakumar-vafa类型在卡拉比野（Calabi-Yau
Gopakumar-Vafa type invariants on Calabi-Yau 4-folds via descendent insertions
论文作者
论文摘要
gopakumar-vafa型不变4倍（仅针对零属而不是平凡），由gromov-witten理论定义，klemm-pandharipande定义了，它们的完整性是猜想。在先前的Cao-Maulik-toda的工作中，$ \ mathrm {dt} _4 $不变式在一个维度稳定的搁板的模量空间上进行了主要插入，以对零GV类型不变属的理论解释。在本文中，我们提出了使用后代插入上述模量空间对One GV类型属不变的属的理论解释。猜想的公式特别意味着对Cy 4倍的零GV类型（等效GW）的非平凡约束，WDVV方程可以证明。
The Gopakumar-Vafa type invariants on Calabi-Yau 4-folds (which are non-trivial only for genus zero and one) are defined by Klemm-Pandharipande from Gromov-Witten theory, and their integrality is conjectured. In a previous work of Cao-Maulik-Toda, $\mathrm{DT}_4$ invariants with primary insertions on moduli spaces of one dimensional stable sheaves are used to give a sheaf theoretical interpretation of the genus zero GV type invariants. In this paper, we propose a sheaf theoretical interpretation of the genus one GV type invariants using descendent insertions on the above moduli spaces. The conjectural formula in particular implies nontrivial constraints on genus zero GV type (equivalently GW) invariants of CY 4-folds which can be proved by the WDVV equation.
