论文标题
Fano叶叶有小代数等级
Fano foliations with small algebraic ranks
论文作者
论文摘要
在本文中，我们研究了$ \ mathbb {q} $ - 阶乘普通投射品种的叶子代数等级。我们首先根据代数等级建立Kobayashi-Ochiai的Fano叶子定理。然后，我们研究了叶的反典型分裂的局部阳性，从seshadri常数方面获得了叶面代数等级的下限。我们描述了那些代数等级略微超过该界限的叶子，并将Fano叶分类为平滑的投射品种，达到了这种界限。最后，我们构建了几个示例来说明总体情况，这特别使我们能够回答Araujo和Druel关于叶子的广义指数的问题。
In this paper we study the algebraic ranks of foliations on $\mathbb{Q}$-factorial normal projective varieties. We start by establishing a Kobayashi-Ochiai's theorem for Fano foliations in terms of algebraic rank. We then investigate the local positivity of the anti-canonical divisors of foliations, obtaining a lower bound for the algebraic rank of a foliation in terms of Seshadri constant. We describe those foliations whose algebraic rank slightly exceeds this bound and classify Fano foliations on smooth projective varieties attaining this bound. Finally we construct several examples to illustrate the general situation, which in particular allow us to answer a question asked by Araujo and Druel on the generalised indices of foliations.
