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Vector bundles over an elliptic curve
 Proc. London Math. Soc
, 1957
"... THE primary purpose of this paper is the study of algebraic vector bundles over an elliptic curve (defined over an algebraically closed field k). The interest of the elliptic curve lies in the fact that it provides the first nontrivial case, Grothendieck (6) having shown that for a rational curve e ..."
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THE primary purpose of this paper is the study of algebraic vector bundles over an elliptic curve (defined over an algebraically closed field k). The interest of the elliptic curve lies in the fact that it provides the first nontrivial case, Grothendieck (6) having shown that for a rational curve
• Vector bundles
"... Course Material and Topics: This course covers the basic theory of differentiable manifolds. A differentiable manifold is a topological space that is locally similar enough to Euclidean space to allow one to do calculus. The tools of manifold theory are indispensable in most major subfields of mathe ..."
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Course Material and Topics: This course covers the basic theory of differentiable manifolds. A differentiable manifold is a topological space that is locally similar enough to Euclidean space to allow one to do calculus. The tools of manifold theory are indispensable in most major subfields of mathematics, and outside of mathematics they are becoming increasingly important to scientists in such diverse areas as economics, computer science, and physics. This course covers basic core material that would be useful for many fields of mathematics. Topics to be covered: • Manifolds
Double vector bundles and duality
"... Abstract. The notions of the dual double vector bundle and the dual double vector bundle morphism are defined. Theorems on canonical isomorphisms are formulated and proved. Several examples are given. 1. Introduction. The notion of a double vector bundle was introduced by Pradines in [3]. The most i ..."
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Abstract. The notions of the dual double vector bundle and the dual double vector bundle morphism are defined. Theorems on canonical isomorphisms are formulated and proved. Several examples are given. 1. Introduction. The notion of a double vector bundle was introduced by Pradines in [3]. The most
and Vector Bundles
, 2006
"... Copying and reprinting. Material in this book may be reproduced by any means for educational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledgment of the source is ..."
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Copying and reprinting. Material in this book may be reproduced by any means for educational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledgment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale. Requests for permission for
VECTOR BUNDLES ON SASAKIAN MANIFOLDS
, 809
"... Abstract. We investigate the analog of holomorphic vector bundles in the context of Sasakian manifolds. 1. ..."
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Abstract. We investigate the analog of holomorphic vector bundles in the context of Sasakian manifolds. 1.
Geometric Quantization of Vector Bundles
"... ABSTRACT. I repeat my definition for quantization of a vector bundle. For the cases of Töplitz and geometric quantization of a compact Kähler manifold, I give a construction for quantizing any smooth vector bundle which depends functorially on a choice of connection on the bundle. ..."
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ABSTRACT. I repeat my definition for quantization of a vector bundle. For the cases of Töplitz and geometric quantization of a compact Kähler manifold, I give a construction for quantizing any smooth vector bundle which depends functorially on a choice of connection on the bundle.
POSITIVITY FOR TORIC VECTOR BUNDLES
"... We show that a Tequivariant vector bundle on a complete toric variety is nef or ample if and only if its restriction to every invariant curve is nef or ample, respectively. Furthermore, we show that nef toric vector bundles have a nonvanishing global section at every point and deduce that the und ..."
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Cited by 4 (2 self)
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We show that a Tequivariant vector bundle on a complete toric variety is nef or ample if and only if its restriction to every invariant curve is nef or ample, respectively. Furthermore, we show that nef toric vector bundles have a nonvanishing global section at every point and deduce
PARABOLIC VECTOR BUNDLES AND EQUIVARIANT VECTOR BUNDLES
, 2001
"... Abstract. Given a complex manifold X, a normal crossing divisor D ⊂ X whose irreducible components D1,..., Ds are smooth, and a choice of natural numbers r = (r1,...,rs), we construct a manifold X(D, r) with an action of a torus Γ and we prove that some full subcategory of the category of Γequivari ..."
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equivariant vector bundles on X(D, r) is equivalent to the category of parabolic vector bundles on (X, D) in which the lengths of the filtrations over each irreducible component of X are given by r. When X is Kaehler, we study the Kaehler cone of X(D, r) and the relation between the corresponding notions of slope
CONSTRUCTION OF EQUIVARIANT VECTOR BUNDLES
, 2004
"... Abstract. Let X be the wonderful compactification of a complex adjoint symmetric space G/K such that rk(G/K) = rk(G) − rk(K). We show how to extend equivariant vector bundles on G/K to equivariant vector bundles on X, generated by their global sections and having trivial higher cohomology groups. ..."
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Cited by 3 (1 self)
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Abstract. Let X be the wonderful compactification of a complex adjoint symmetric space G/K such that rk(G/K) = rk(G) − rk(K). We show how to extend equivariant vector bundles on G/K to equivariant vector bundles on X, generated by their global sections and having trivial higher cohomology groups
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