论文标题
重言式希尔伯特计划不变的卡拉比 - 远4倍通过虚拟回调
Tautological Hilbert scheme invariants of Calabi-Yau 4-folds via virtual pullback
论文作者
论文摘要
令$ x $为calabi-yau 4倍和$ d $ a平滑连接的除数。我们考虑$ L = \ Mathcal {o} _x（d）$的重言式捆绑包上的Hilbert Shemes $ x $上的点及其计数不变性，通过针对虚拟类集成Euler类而定义了不变。我们将这些不变的人与Maulik-Nekrasov-Okounkov-Pandharipande的“ Hilbert Shemes of Hilbert Shemes of Soints of Points of Boints”的不变性联系起来，并通过Virtual Roupback Technique在$ d $上，并确认了CAO-kool的猜想。还采用了相同的策略来获得一个虚拟的回调公式，用于一维稳定滑轮的重言式不变术。这反过来赋予了CAO，Maulik和Toda的作品中研究的主要和后代不变性的非平凡身份。
Let $X$ be a Calabi-Yau 4-fold and $D$ a smooth connected divisor on it. We consider tautological bundles of $L=\mathcal{O}_X(D)$ on Hilbert schemes of points on $X$ and their counting invariants defined by integrating the Euler classes against the virtual classes. We relate these invariants to Maulik-Nekrasov-Okounkov-Pandharipande's invariants of Hilbert schemes of points on $D$ by virtual pullback technique and confirm a conjecture of Cao-Kool. The same strategy is also applied to obtain a virtual pullback formula for tautological invariants of one dimensional stable sheaves. This in turn gives a nontrivial identity on primary and descendent invariants as studied in the works of Cao, Maulik and Toda.
