Locally Unsplit Families of Rational Curves of Large Anticanonical Degree on Fano Manifolds

被引：17

作者：

Casagrande, Cinzia ^{[1
]}

Druel, Stephane ^{[2
]}

机构：

[1] Univ Turin, Dipartimento Matemat, I-10123 Turin, Italy

[2] Univ Grenoble 1, CNRS, UMR 5582, Inst Fourier, F-38402 St Martin Dheres, France

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2015年 / 2015卷 / 21期

关键词：

VARIETIES; DIVISOR;

D O I：

10.1093/imrn/rnv011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we address Fano manifolds of dimension n >= 3 with a locally unsplit dominating family of rational curves of anticanonical degree n. We first observe that their Picard number is at most 3, and then we provide a classification of all cases with maximal Picard number. We also give examples of locally unsplit dominating families of rational curves whose varieties of minimal tangents at a general point are singular.

引用

页码：10756 / 10800

页数：45

共 32 条

[1]

Andreatta M., 1997, Algebraic GeometrySanta Cruz, V62, P153

[2]

[Anonymous], 1977, Graduate Texts in Mathematics

[3]

[Anonymous], 2013, Cambridge Tracts in Mathematics

[4] Rational curves of minimal degree and characterizations of projective spaces [J].