论文标题
Fano品种的核心性
Coregularity of Fano varieties
论文作者
论文摘要
Fano品种的规律性，用$ {\ rm reg}（x）$表示，是$ x $上的log calabi-yau结构的双重复合体的最大维度。核心性定义为\ [{\ rm coreg}（x）：= \ dim x- {\ rm reg}（x）-1。 \]核心性是规律性的互补维度。我们预计，Fano品种的核心性在很大程度上是$ x $的几何形状。在本说明中，我们回顾了Fano品种的历史，举例说明，调查一些重要的定理，引入核心性，并提出有关Fano品种的不变的一些问题。
The regularity of a Fano variety, denoted by ${\rm reg}(X)$, is the largest dimension of the dual complex of a log Calabi--Yau structure on $X$. The coregularity is defined to be \[ {\rm coreg}(X):= \dim X - {\rm reg}(X)-1. \] The coregularity is the complementary dimension of the regularity. We expect that the coregularity of a Fano variety governs, to a large extent, the geometry of $X$. In this note, we review the history of Fano varieties, give some examples, survey some important theorems, introduce the coregularity, and propose several problems regarding this invariant of Fano varieties.
