论文标题
镜子p = W猜想和扩展的Fano/Landau-Ginzburg对应关系
Mirror P=W conjecture and extended Fano/Landau-Ginzburg correspondence
论文作者
论文摘要
镜子p = w猜想是由硬katzarkov-przyjalkowski制定的，可以预测在镜像对称性的背景下，重量和反向过滤之间的对应关系。在本文中，我们通过fano对$（x，d）$的镜子对称镜头重新审视了这个猜想，其中$ x $是一种流畅的fano品种，$ d $是一个简单的正常交叉分裂。我们将其镜像作为Landau-Ginzburg（LG）模型的多潜电类似物引入，我们称之为混合LG模型。预计该型号将捕获$ d $的所有不可还原组件的镜子。我们研究了基于Katzarkov-Kontsevich-Pantev的工作，研究了拓扑方面，尤其是不良过滤和混合LG模型的霍奇理论。作为一种应用，我们发现了在混合LG模型的反向过滤的多重性上有趣的上限。此外，我们提出了同源镜子对称性猜想的相对版本，并解释了镜子p = w猜想是如何自然出现的。
The mirror P=W conjecture, formulated by Harder-Katzarkov-Przyjalkowski, predicts a correspondence between weight and perverse filtrations in the context of mirror symmetry. In this paper, we revisit this conjecture through the lens of mirror symmetry for a Fano pair $(X,D)$, where $X$ is a smooth Fano variety and $D$ is a simple normal crossing divisor. We introduce its mirror object as a multi-potential analogue of a Landau-Ginzburg (LG) model, which we call the hybrid LG model. This model is expected to capture the mirrors of all irreducible components of $D$. We study the topological aspects, particularly the perverse filtration, and the Hodge theory of hybrid LG models, building upon the work of Katzarkov-Kontsevich-Pantev. As an application, we discover an interesting upper bound on the multiplicativity of the perverse filtration for a hybrid LG model. Additionally, we propose a relative version of the homological mirror symmetry conjecture and explain how the mirror P=W conjecture naturally emerges from it.
