scholarly journals Realization of Chern classes by subvarieties with certain singularities

1980 ◽  
Vol 80 ◽  
pp. 49-74 ◽  
Author(s):  
Hiroshi Morimoto
Keyword(s):  
Vector Bundles ◽  
Chern Classes ◽  
Algebraic Varieties ◽  
Stein Manifolds ◽  
Holomorphic Vector Bundles ◽  
Definition Of

In this paper we are concerned with subvarieties which realize Chern classes of holomorphic vector bundles. The existence of these subvarieties is known in some cases (for instance, see A. Grotheridieck [2] for projective algebraic varieties and M. Cornalba and P. Griffiths [1] for Stein manifolds). In the present paper we realize Chern classes by subvarieties with singularities of a certain type. Our main theorem is as follows (see Def. 1.1.3 for the definition of quasilinear subvarieties).

NUMERICALLY FLAT HIGGS VECTOR BUNDLES

2007 ◽  
Vol 09 (04) ◽  
pp. 437-446 ◽  
Author(s):  
UGO BRUZZO ◽  
BEATRIZ GRAÑA OTERO
Keyword(s):  
Vector Bundles ◽  
Higgs Bundle ◽  
Higgs Bundles ◽  
Chern Classes ◽  
Related Notion ◽  
Suitable Definition ◽  
Definition Of

After providing a suitable definition of numerical effectiveness for Higgs bundles, and a related notion of numerical flatness, in this paper we prove, together with some side results, that all Chern classes of a Higgs-numerically flat Higgs bundle vanish, and that a Higgs bundle is Higgs-numerically flat if and only if it is has a filtration whose quotients are flat stable Higgs bundles. We also study the relation between these numerical properties of Higgs bundles and (semi)stability.

scholarly journals A Construction of Chern Classes of Parabolic Vector Bundles

2013 ◽  
Vol 42 (3) ◽  
pp. 1111-1122 ◽  
Author(s):  
Indranil Biswas ◽  
Ajneet Dhillon
Keyword(s):  
Vector Bundles ◽  
Chern Classes

scholarly journals Chern classes of tensor products

2016 ◽  
Vol 27 (10) ◽  
pp. 1650079 ◽  
Author(s):  
Laurent Manivel
Keyword(s):  
Vector Bundles ◽  
Tensor Products ◽  
Chern Classes ◽  
Explicit Formulas

We prove explicit formulas for Chern classes of tensor products of virtual vector bundles, whose coefficients are given by certain universal polynomials in the ranks of the two bundles.

Hermitian–Einstein metrics and jumping lines forSp(n+1)-homogeneous bundles over ℙ2n+1

1993 ◽  
Vol 114 (3) ◽  
pp. 443-451
Author(s):  
Al Vitter
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Vector Bundles ◽  
Einstein Metrics ◽  
Einstein Metric ◽  
Holomorphic Vector Bundles ◽  
Kähler Form ◽  
Points Of View ◽  
The Stability ◽  
Complex Projective

Stable holomorphic vector bundles over complex projective space ℙnhave been studied from both the differential-geometric and the algebraic-geometric points of view.On the differential-geometric side, the stability ofE-→ ℙncan be characterized by the existence of a unique hermitian–Einstein metric onE, i.e. a metric whose curvature matrix has trace-free part orthogonal to the Fubini–Study Kähler form of ℙn(see [6], [7], and [13]). Very little is known about this metric in general and the only explicit examples are the metrics on the tangent bundle of ℙnand the nullcorrelation bundle (see [9] and [10]).

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