Metrics on semistable and numerically effective Higgs bundles

被引：32

作者：

Bruzzo, Ugo ^{[1
]}

Grana Otero, Beatriz ^{[2
,3
]}

机构：

[1] Scuola Int Super Studi Avanzati, Ist Nazl Fis Nucl, Sez Trieste, I-34013 Trieste, Italy

[2] Univ Salamanca, Dept Math, E-37008 Salamanca, Spain

[3] Univ Salamanca, Inst Fis Fundamental & Matemat, E-37008 Salamanca, Spain

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2007年 / 612卷

关键词：

D O I：

10.1515/CRELLE.2007.084

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide notions of numerical effectiveness and numerical flatness for Higgs vector bundles on compact Kahler manifolds in terms of fibre metrics. We prove several properties of bundles satisfying such conditions and in particular we show that numerically flat Higgs bundles have vanishing Chem classes, and that they admit filtrations whose quotients are stable flat Higgs bundles. We compare these definitions with those previously given in the case of projective varieties. Finally we study the relations between numerically effectiveness and semistability, establishing semistability criteria for Higgs bundles on projective manifolds of any dimension.

引用

页码：59 / 79

页数：21

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