A real algebraic vector bundle is strongly algebraic whenever its total space is affine

1995 ◽  
pp. 117-119 ◽  
Author(s):  
J. Huisman
Keyword(s):  
Vector Bundle ◽  
Total Space ◽  
Algebraic Vector Bundle ◽  
Algebraic Vector

scholarly journals Coherent Systems and Brill–Noether Theory

2003 ◽  
Vol 14 (07) ◽  
pp. 683-733 ◽  
Author(s):  
S. B. Bradlow ◽  
O. García-Prada ◽  
V. Muñoz ◽  
P. E. Newstead
Keyword(s):  
Vector Bundle ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Coherent System ◽  
Coherent Systems ◽  
Stable Bundles ◽  
Algebraic Vector Bundle ◽  
Picard Groups ◽  
Algebraic Vector ◽  
The Stability

Let X be a curve of genus g. A coherent system on X consists of a pair (E,V), where E is an algebraic vector bundle over X of rank n and degree d and V is a subspace of dimension k of the space of sections of E. The stability of the coherent system depends on a parameter α. We study the variation of the moduli space of coherent systems when we move the parameter. As an application, we analyze the cases k=1,2,3 and n=2 explicitly. For small values of α, the moduli spaces of coherent systems are related to the Brill–Noether loci, the subschemes of the moduli spaces of stable bundles consisting of those bundles with at least a prescribed number of independent sections. The study of coherent systems is applied to find the dimension, prove the irreducibility, and in some cases calculate the Picard groups of the Brill–Noether loci with k≤3.

Normal bundles in flag bundles

1981 ◽  
Vol 90 (3) ◽  
pp. 395-402
Author(s):  
Samuel A. Ilori
Keyword(s):  
Vector Bundle ◽  
Normal Bundle ◽  
Closed Field ◽  
Projective Varieties ◽  
Algebraically Closed Field ◽  
Algebraic Vector Bundle ◽  
Algebraic Vector ◽  
Normal Bundles ◽  
Tangent Bundles

AbstractLet i: Y ↪ X be an inclusion map of non-singular irreducible algebraic quasi-projective varieties defined over an algebraically closed field. Let E be an algebraic vector bundle over X and H be a sub-bundle of the induced bundle, i*E. If j:F(H) ↪ F(E) is the corresponding inclusion map of (incomplete) flag bundles, then we derive the normal bundle N(F(H), F(E)) in terms of the bundles H and E, the tangent bundles of Y and X as well as the tautological bundles over F(H).

scholarly journals Stratified-algebraic vector bundles

2018 ◽  
Vol 2018 (745) ◽  
pp. 105-154 ◽  
Author(s):  
Wojciech Kucharz ◽  
Krzysztof Kurdyka
Keyword(s):  
Vector Bundle ◽  
Algebraic Variety ◽  
Pairwise Disjoint ◽  
Vector Bundles ◽  
Real Algebraic Variety ◽  
Finite Collection ◽  
Algebraic Vector Bundle ◽  
Algebraic Vector

Abstract We investigate stratified-algebraic vector bundles on a real algebraic variety X. A stratification of X is a finite collection of pairwise disjoint, Zariski locally closed subvarieties whose union is X. A topological vector bundle ξ on X is called a stratified-algebraic vector bundle if, roughly speaking, there exists a stratification {\mathcal{S}} of X such that the restriction of ξ to each stratum S in {\mathcal{S}} is an algebraic vector bundle on S. In particular, every algebraic vector bundle on X is stratified-algebraic. It turns out that stratified-algebraic vector bundles have many surprising properties, which distinguish them from algebraic and topological vector bundles.

Vector bundles that fill n-space

1965 ◽  
Vol 61 (4) ◽  
pp. 869-875 ◽  
Author(s):  
S. A. Robertson ◽  
R. L. E. Schwarzenberger
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Total Space

The idea of exact filling bundle may be described roughly as follows. Suppose that ξk is a vector bundle with fibre Rk, total space E(ξk) and base X. We say that ξk is a real k-plane bundle on X. Let in be the trivial n-plane bundle on X so that E(in) = X × Rn. A bundle monomorphism j: ξk → in defines a map : E(ξk)→Rn obtained by composition of the embedding E(ξk)→E(in) and the product projection E(in) → Rn. The map represents each fibre of ξk as a k-plane in Rn.

The hypoelliptic Laplacian on X = G/K

2011 ◽  
Author(s):  
Jean-Michel Bismut
Keyword(s):  
Vector Bundle ◽  
Symmetric Space ◽  
Dirac Operator ◽  
Clifford Algebras ◽  
Second Order ◽  
Total Space ◽  
Hypoelliptic Operator ◽  
Heisenberg Algebras

This chapter constructs the hypoelliptic Laplacian ℒbX > 0 acting on the total space of a vector bundle TX ⊕ N ≃ g over the symmetric space X = G/K. The operator ℒbX is obtained using general constructions involving Clifford algebras and Heisenberg algebras, and also the Dirac operator of Kostant. The end result is the elliptic Laplacian 𝓛 X on X as well as the hypoelliptic Laplacian ℒbX, which is a second order hypoelliptic operator acting on X^. Among other things, this chapter gives a key formula relating 𝓛 XℒbX, as well as various formulas involving the operator ℒbX+La.

scholarly journals Structure presque-transverse intégrable

1988 ◽  
Vol 37 (2) ◽  
pp. 173-177
Author(s):  
Tong Van Duc
Keyword(s):  
Vector Bundle ◽  
Total Space ◽  
Transversal Structure

We find conditions for which a manifold endowed with an integrable almost transversal structure is the total space of a vector bundle isomorphic to the transversal bundle of a foliation.

scholarly journals HODGE STRUCTURES OF THE MODULI SPACES OF PAIRS

2010 ◽  
Vol 21 (11) ◽  
pp. 1505-1529 ◽  
Author(s):  
VICENTE MUÑOZ
Keyword(s):  
Vector Bundle ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Hodge Structure ◽  
Projective Curve ◽  
Hodge Structures ◽  
Smooth Projective Curve ◽  
Stable Vector Bundles ◽  
Algebraic Vector

Let X be a smooth projective curve of genus g ≥ 2 over ℂ. Fix n ≥ 2, d ∈ ℤ. A pair (E, ϕ) over X consists of an algebraic vector bundle E of rank n and degree d over X and a section ϕ ∈ H0(E). There is a concept of stability for pairs which depends on a real parameter τ. Let [Formula: see text] be the moduli space of τ-semistable pairs of rank n and degree d over X. Here we prove that the cohomology groups of [Formula: see text] are Hodge structures isomorphic to direct summands of tensor products of the Hodge structure H1(X). This implies a similar result for the moduli spaces of stable vector bundles over X.

On complex vector bundles on rational threefolds

1985 ◽  
Vol 97 (2) ◽  
pp. 279-288 ◽  
Author(s):  
Constantin BẮnicẮ ◽  
Mihai Putinar
Keyword(s):  
Vector Bundle ◽  
Algebraic Structure ◽  
Vector Bundles ◽  
Topological Type ◽  
Rational Surface ◽  
Chern Classes ◽  
Complex Vector Bundle ◽  
Complex Vector ◽  
Algebraic Vector ◽  
Rank 2

It is known [14] that every topological complex vector bundle on a smooth rational surface admits an algebraic structure. In [10] one constructs algebraic vector bundles of rank 2 on with arbitrary Chern classes c1, c2 subject to the necessary topological condition c1 c2 = 0 (mod 2). However, in dimensions greater than 2 the Chern classes don't determine the topological type of a vector bundle. In [2] one classifies the topological complex vector bundles of rank 2 on and one proves that any such bundle admits an algebraic structure.

Sign in / Sign up

Export Citation Format

Share Document