AI 中文总结
本文介绍通过平滑拟Fano流形法向交叉并集构造Calabi-Yau流形的进展，给出具无界第二贝蒂数、极小赫奇数的Calabi-Yau三维流形及高维非凯勒示例，阐释Landau-Ginzburg模型在镜像构造中的作用
AI 中文摘要
我们将讨论自2010年该方法被引入物理学界以来，通过平滑拟Fano流形的法向交叉并集来构造Calabi-Yau流形的相关进展。我们描述了具有无界第二贝蒂数及极小赫奇数的Calabi-Yau三维流形的构造，以及维度大于三的首个非凯勒示例的构造，同时阐释了Landau-Ginzburg模型在镜像构造中的作用。
英文摘要
We discuss developments in the construction of Calabi--Yau manifolds by smoothing normal crossing unions of quasi-Fano manifolds, following the introduction of this method to the physics community in 2010. We describe constructions of Calabi--Yau threefolds with unbounded second Betti numbers and with very small Hodge numbers, as well as the first non-Kähler examples in dimensions greater than three. The role of Landau--Ginzburg models in mirror constructions is also explained.
Comments12 pages
