Coregularity of Fano varieties

Pub Date : 2024-02-10 DOI:10.1007/s10711-023-00882-z

引用次数: 0

Abstract

The absolute regularity of a Fano variety, denoted by $\hat{\textrm{reg}}(X)$ , is the largest dimension of the dual complex of a log Calabi–Yau structure on X. The absolute coregularity is defined to be $$\begin{aligned} \hat{\textrm{coreg}}(X):= \dim X - \hat{\textrm{reg}}(X)-1. \end{aligned}$$ 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 theorems, introduce the coregularity, and propose several problems regarding this invariant of Fano varieties.

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法诺变种的内核性

摘要法诺综的绝对正则性用 \(\hat\textrm{reg}}(X)\ 表示。绝对正则性的定义是 $$\begin{aligned}\hat{textrm{coreg}}(X):= \dim X - \hat{textrm{reg}}(X)-1.\end{aligned}$$ 核心规则性是规则性的补充维度。在本注释中，我们回顾了法诺变的历史，举了一些例子，考察了一些定理，介绍了核正则性，并提出了有关法诺变这一不变量的几个问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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