Geometric Manin's conjecture and rational curves

被引：22

作者：

Lehmann, Brian ^{[1
]}

Tanimoto, Sho ^{[2
,3
]}

机构：

[1] Boston Coll, Dept Math, 1400 Commonwealth Ave, Chestnut Hill, MA 02467 USA

[2] Kumamoto Univ, Dept Math, Fac Sci, Kurokami 2-39-1, Kumamoto 8608555, Japan

[3] Kumamoto Univ, Prior Org Innovat & Excellence, Kumamoto, Japan

来源：

COMPOSITIO MATHEMATICA | 2019年 / 155卷 / 05期

基金：

美国国家科学基金会;

关键词：

rational curves; Manin's conjecture; Fujita invariant; POINTS; VARIETIES; NUMBER; SPACES; IRREDUCIBILITY; HYPERSURFACES; FAMILIES; SURFACES;

D O I：

10.1112/S0010437X19007103

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a smooth projective Fano variety over the complex numbers. We study the moduli space of rational curves on X using the perspective of Manin's conjecture. In particular, we bound the dimension and number of components of spaces of rational curves on X. We propose a geometric Manin's conjecture predicting the growth rate of a counting function associated to the irreducible components of these moduli spaces.

引用

页码：833 / 862

页数：30

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