论文标题
加拉比（Calabi-Yau）的重言式稳定对不变4倍
Tautological stable pair invariants of Calabi-Yau 4-folds
论文作者
论文摘要
让$ x $成为calabi-yau 4倍和$ d $ a平滑的除数。我们认为在Le Potier稳定对的Moduli空间上，与$ L = \ Mathcal {O} _x（d）$相关的重言式复合物，并通过将Euler类集成到虚拟类中来定义其计数不变。我们猜想使用零d $的零gopakumar-vafa属和一个$ d $ $ x $的gopakumar-vafa类型不变的属的生成系列的公式，我们在几个示例中验证了这一点。当$ x $是本地解决的Conifold时，我们的猜想在PT室内重现了Cao-kool-Monavari的猜想公式。在JS室内，我们完全确定不变性并确认我们以前的猜想之一。
Let $X$ be a Calabi-Yau 4-fold and $D$ a smooth divisor on it. We consider tautological complex associated with $L=\mathcal{O}_X(D)$ on the moduli space of Le Potier stable pairs and define its counting invariant by integrating the Euler class against the virtual class. We conjecture a formula for their generating series expressed using genus zero Gopakumar-Vafa invariants of $D$ and genus one Gopakumar-Vafa type invariants of $X$, which we verify in several examples. When $X$ is the local resolved conifold, our conjecture reproduces a conjectural formula of Cao-Kool-Monavari in the PT chamber. In the JS chamber, we completely determine the invariants and confirm one of our previous conjectures.
