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 non-trivial case, Grothendieck (6) having shown that for a rational curve

We construct vector bundles R rk

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

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

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Abstract. We investigate the analog of holomorphic vector bundles in the context of Sasakian manifolds. 1.

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.

We show that a T-equivariant 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

-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

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