论文标题
关于分类枚举不变性的莫里塔不变性
On the Morita invariance of Categorical Enumerative Invariants
论文作者
论文摘要
分类枚举不变性（CEI）是与Unital，循环，光滑的$ A_ \ Infty $类别相关的不变性，并且其非交换性Hodge过滤的分裂。在本文中，我们将CEI的定义扩展到了Calabi-yau $ a_ \ indy $ - 分类。此外，我们制定并证明了CEI的Morita不变性。作为证明的一部分，我们开发了为卡拉比YAU类别构建Unital和循环模型的工具。特别是，我们证明了Kontsevich-Soibelman的Darboux定理的一个Unital版本。作为应用程序，我们在一些新示例中计算CEI。同样，当应用于相干滑轮的派生类别时，我们的结果会产生新的不变，适当的卡拉比Yau 3倍的新不变性。
Categorical Enumerative Invariants (CEI) are invariants associated with a unital, cyclic, smooth $A_\infty$-category and a splitting of its non-commutative Hodge filtration. In this paper, we extend the definition of CEI to Calabi-Yau $A_\infty$-categories with a splitting. Moreover, we formulate and prove the Morita invariance of CEI. As part of our proof, we develop tools to construct unital and cyclic models for Calabi-Yau categories. In particular, we prove a unital version of Kontsevich-Soibelman's Darboux theorem. As an application, we compute CEI in some new examples. Also, when applied to derived categories of coherent sheaves, our results yield new invariants of smooth, proper Calabi-Yau 3-folds.
