scholarly journals A cohomological classification of vector bundles on smooth affine threefolds

2014 ◽  
Vol 163 (14) ◽  
pp. 2561-2601 ◽  
Author(s):  
Aravind Asok ◽  
Jean Fasel
Keyword(s):  
Vector Bundles ◽  
Smooth Affine

scholarly journals Fano 3-folds from homogeneous vector bundles over Grassmannians

2021 ◽  
Author(s):  
Lorenzo De Biase ◽  
Enrico Fatighenti ◽  
Fabio Tanturri
Keyword(s):  
Vector Bundles ◽  
Homogeneous Vector

AbstractWe rework the Mori–Mukai classification of Fano 3-folds, by describing each of the 105 families via biregular models as zero loci of general global sections of homogeneous vector bundles over products of Grassmannians.

scholarly journals Two-Categorical Bundles and their Classifying Spaces

2012 ◽  
Vol 10 (2) ◽  
pp. 299-369 ◽  
Author(s):  
Nils A. Baas ◽  
Marcel Bökstedt ◽  
Tore August Kro
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Vector Spaces ◽  
Bundle Theory ◽  
Classifying Spaces ◽  
Classifying Space ◽  
Principal Bundles

AbstractFor a 2-category 2C we associate a notion of a principal 2C-bundle. For the 2-category of 2-vector spaces, in the sense of M.M. Kapranov and V.A. Voevodsky, this gives the 2-vector bundles of N.A. Baas, B.I. Dundas and J. Rognes. Our main result says that the geometric nerve of a good 2-category is a classifying space for the associated principal 2-bundles. In the process of proving this we develop powerful machinery which may be useful in further studies of 2-categorical topology. As a corollary we get a new proof of the classification of principal bundles. Another 2-category of 2-vector spaces has been proposed by J.C. Baez and A.S. Crans. A calculation using our main theorem shows that in this case the theory of principal 2-bundles splits, up to concordance, as two copies of ordinary vector bundle theory. When 2C is a cobordism type 2-category we get a new notion of cobordism-bundles which turns out to be classified by the Madsen–Weiss spaces.

scholarly journals The group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra

2019 ◽  
Vol 30 (11) ◽  
pp. 1950057 ◽  
Author(s):  
M. Izumi ◽  
T. Sogabe
Keyword(s):  
Automorphism Group ◽  
Vector Bundles ◽  
Group Structure ◽  
Cuntz Algebra ◽  
Classifying Space ◽  
Cuntz Algebras ◽  
K Theory ◽  
Continuous Fields

We determine the group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra [Formula: see text] for finite [Formula: see text] in terms of K-theory. We show that there is an example of a space for which the homotopy set is a noncommutative group, and hence, the classifying space of the automorphism group of the Cuntz algebra for finite [Formula: see text] is not an H-space. We also make an improvement of Dadarlat’s classification of continuous fields of the Cuntz algebras in terms of vector bundles.

CLASSIFICATION OF REAL ALGEBRAIC VECTOR BUNDLES OVER THE REAL ANISOTROPIC CONIC

2005 ◽  
Vol 16 (10) ◽  
pp. 1207-1220 ◽  
Author(s):  
INDRANIL BISWAS ◽  
D. S. NAGARAJ
Keyword(s):  
Vector Bundles ◽  
Complete Classification ◽  
Real Numbers ◽  
The Real ◽  
Isomorphism Classes ◽  
Algebraic Vector

We give a complete classification of isomorphism classes of real algebraic vector bundles over the scheme defined by a nondegenerate anisotropic conic defined over the field of real numbers.

On the Classification of Lie Pseudo-Algebras

1970 ◽  
Vol 22 (5) ◽  
pp. 905-915 ◽  
Author(s):  
Ngö van Quê
Keyword(s):  
Vector Bundle ◽  
Exact Sequence ◽  
Tensor Product ◽  
Vector Bundles ◽  
Canonical Morphism ◽  
Image Position

For every ( differentiable) bundle E over a manifold M, Jk(E) denotes the set of all k-jets of local (differentiable) sections of the bundle E. Jk(E) is a bundle over M such that if X is a section of E, thenis a (differentiable) section of Jk(E). If E is a vector bundle, Jk(E) is a vector bundle and we have the canonical exact sequence of vector bundleswhere Sk(T*) is the symmetric Whitney tensor product of the cotangent vector bundle T* of M. and π is the canonical morphism which associates to each k-jet of section its jet of inferior order.

scholarly journals Classification of smooth affine spherical varieties

2006 ◽  
Vol 11 (3) ◽  
pp. 495-516 ◽  
Author(s):  
Friedrich Knop ◽  
Bart Van Steirteghem
Keyword(s):  
Spherical Varieties ◽  
Smooth Affine

scholarly journals Homology of SL2 over function fields I: Parabolic subcomplexes

2018 ◽  
Vol 2018 (739) ◽  
pp. 159-205
Author(s):  
Matthias Wendt
Keyword(s):  
Vector Bundles ◽  
Function Fields ◽  
Equivalence Classes ◽  
Isotropy Group ◽  
Closed Field ◽  
Explicit Formulas ◽  
Algebraically Closed Field ◽  
Group Homology ◽  
Equivariant Homology ◽  
Smooth Affine

Abstract The present paper studies the group homology of the groups {\operatorname{SL}_{2}(k[C])} and {\operatorname{PGL}_{2}(k[C])} , where {C=\overline{C}\setminus\{P_{1},\dots,P_{s}\}} is a smooth affine curve over an algebraically closed field k. It is well known that these groups act on a product of trees and the quotients can be described in terms of certain equivalence classes of rank two vector bundles on the curve {\overline{C}} . There is a natural subcomplex consisting of cells with suitably non-trivial isotropy group. The paper provides explicit formulas for the equivariant homology of this “parabolic subcomplex”. These formulas also describe group homology of {\operatorname{SL}_{2}(k[C])} above degree s, generalizing a result of Suslin in the case {s=1} .

scholarly journals LOW RANK VECTOR BUNDLES ON THE GRASSMANNIAN G(1,4)

2009 ◽  
Vol 06 (07) ◽  
pp. 1103-1114 ◽  
Author(s):  
FRANCESCO MALASPINA
Keyword(s):  
Finite Number ◽  
Vector Bundles ◽  
Low Rank ◽  
Coherent Sheaves ◽  
Splitting Criterion ◽  
Rank 2 ◽  
Rank Vector ◽  
Rank 2 Vector Bundles

Here we define the concept of L-regularity for coherent sheaves on the Grassmannian G(1,4) as a generalization of Castelnuovo–Mumford regularity on Pn. In this setting we prove analogs of some classical properties. We use our notion of L-regularity in order to prove a splitting criterion for rank 2 vector bundles with only a finite number of vanishing conditions. In the second part, we give the classification of rank 2 and rank 3 vector bundles without "inner" cohomology (i.e. [Formula: see text] for any i = 2,3,4) on G(1,4) by studying the associated monads.

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