Rational Curves on Foliated Varieties

被引：21

作者：

Bogomolov, Fedor ^{[1
,2
]}

McQuillan, Michael ^{[3
]}

机构：

[1] NYU, Courant Inst Math Sci, Warren Weaver Hall,Off 602,251 Mercer St, New York, NY 10012 USA

[2] Natl Res Univ, Higher Sch Econ, AG Lab, 7 Vavilova Str, Moscow 117312, Russia

[3] Univ Roma Tor Vergata, Dept Math, Sogene Bldg,Via Ric Sci 1, I-00133 Rome, Italy

来源：

FOLIATION THEORY IN ALGEBRAIC GEOMETRY | 2016年

关键词：

Frobenius (theorem); (foliated) (log) canonical singularities; Algorithmic resolution; Graphic neighbourhood; Ample (vector) bundle; Frobenius (map); Bend and break; p-adic; Rationally connected; Cone of curves; MODELS;

D O I：

10.1007/978-3-319-24460-0_2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The article refines and generalises the study of deformations of a morphism along a foliation begun by Y. Miyaoka, [Mi2]. The key ingredients are the algebrisation of the graphic neighbourhood, see Fact 3.3.1, which reduces the problem from the transcendental to the algebraic, and a p-adic variation of Mori's bend and break in order to overcome the "naive failure", see Remark 3.2.3, of the method in the required generality. Qualitatively the results are optimal for foliations of all ranks in all dimensions, and are quantitatively optimal for foliations by curves, for which the further precision of a cone theorem is provided.

引用

页码：21 / 51

页数：31

共 20 条

[1]

[Anonymous], 1983, Progr. Math

[2]

[Anonymous], 1999, RATIONAL CURVES ALGE

[3]

[Anonymous], 1998, Pub. Math. IHES.

[4]

Arakelov S.J., 1971, IZV AKAD NAUK SSSR M, V35, P1269, DOI 10.1070/IM1971v005n06ABEH001235

[5] Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant [J].

Bierstone, E ;

Milman, PD .

INVENTIONES MATHEMATICAE, 1997, 128 (02) :207-302

[6] HOLOMORPHIC TENSORS AND VECTOR-BUNDLES ON PROJECTIVE VARIETIES [J].

BOGOMOLOV, FA .

MATHEMATICS OF THE USSR-IZVESTIYA, 1979, 13 (03) :499-555

[7]

Bogomolov FA, 1977, SOV MATH DOKL, V18, P279

[8]

Bost JB, 2001, PUBL MATH, P161

[9] Minimal models of foliated algebraic surfaces [J].

Brunella, M .

BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1999, 127 (02) :289-305

[10] Every rationally connected variety over the function field of a curve has a rational point [J].

De Jong, AJ ;

Starr, J .

AMERICAN JOURNAL OF MATHEMATICS, 2003, 125 (03) :567-580

← 1 2 →