Stability and holomorphic connections on vector bundles over LVMB manifolds

被引：1

作者：

Biswas, Indranil ^{[1
]}

Dumitrescu, Sorin ^{[2
]}

Meersseman, Laurent ^{[3
]}

机构：

[1] Tata Inst Fundamental Res, Sch Math, Homi Bhabha Rd, Mumbai 400005, Maharashtra, India

[2] Univ Cote dAzur, CNRS, LJAD, Nice, France

[3] Univ Angers, Lab Angevin Rech Math, Univ Bretagne Loire, F-49045 Angers, France

来源：

COMPTES RENDUS MATHEMATIQUE | 2020年 / 358卷 / 02期

关键词：

COMPACT COMPLEX-MANIFOLDS;

D O I：

10.5802/crmath.24

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize all LVMB manifolds X such that the holomorphic tangent bundle TX is spanned at the generic point by a family of global holomorphic vector fields, each of them having non-empty zero locus. We deduce that holomorphic connections on semi-stable holomorphic vector bundles over LVMB manifolds with this previous property are always flat.

引用

页码：151 / 157

页数：7

共 14 条

[1]

ATIYAH MF, 1957, T AM MATH SOC, V85, P181

[2]

Biswas I., 2019, EUR J MATH, P40879

[3] Compact complex manifolds: an extension of Meersseman's and Lopez de Medrano-Verjovsky's construction [J].

Bosio, F .

ANNALES DE L INSTITUT FOURIER, 2001, 51 (05) :1259-+

[4] Real quadrics in Cn, complex manifolds and convex polytopes [J].

Bosio, Frederic ;

Meersseman, Laurent .

ACTA MATHEMATICA, 2006, 197 (01) :53-127

[5]

BRINZANESCU V, 1996, LECT NOTES MATH, V1624

[6] HERMITIAN-EINSTEIN CONNECTIONS AND STABLE VECTOR-BUNDLES OVER COMPACT COMPLEX-SURFACES [J].

BUCHDAHL, NP .

MATHEMATISCHE ANNALEN, 1988, 280 (04) :625-648

[7] THE 1-FORM OF TORSION OF A COMPACT HERMITIAN MANIFOLD [J].

GAUDUCHON, P .

MATHEMATISCHE ANNALEN, 1984, 267 (04) :495-518

[8]

KOBAYASHI S., 1987, PUBLICATIONS MATH SO, V15

[9]

Lubke M., 1995, KOBAYASHI HITCHIN CO

[10] A new geometric construction of compact complex manifolds in any dimension [J].

Meersseman, L .

MATHEMATISCHE ANNALEN, 2000, 317 (01) :79-115

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