May 25, 2017 · The notion of vector bundle in algebraic geometry. Usually characterized in terms of its sheaf of sections on the locally ringed site (with structure sheaf 𝒪 \mathcal{O}) of the given …

In mathematics, vector bundles on algebraic curves may be studied as holomorphic vector bundles on compact Riemann surfaces, which is the classical approach, or as locally free …

Jul 19, 2024 · Analytic and algebraic vector bundles are equivalent on a complete algebraic variety (see the Comparison Theorem in algebraic geometry). Topological vector bundles do …

A vector bundle $\pi : V \to S$ over $S$ is an affine morphism of schemes such that $\pi _*\mathcal{O}_ V$ is endowed with the structure of a graded $\mathcal{O}_ S$-algebra $\pi …

In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a …

May 12, 2024 · Given some context of geometry, then a vector bundle is a collection of vector spaces that varies in a geometric way over a given base space X: over each element x ∈ X …

There is a natural rank n algebraic vector bundle E on X provided with an embedding in the trivial rank N +1 dimensional vector bundle ON+1 X (in the special case n = 1, this is O PN (−1) ⊂ O …

In mathematics, a holomorphic vector bundle is a complex vector bundle over a complex manifold X such that the total space E is a complex manifold and the projection map π : E → X is …

Jan 1, 1985 · This chapter reviews the results on algebraic vector bundles. In the theory of algebraic vector bundles, one of the most important and difficult problems is to find a fine …

VECTOR BUNDLES. 1. The definition of a vector bundle The de nitions below can be applied to any geometric category that contains vector spaces (topological spaces, smooth varieties, …

In the first section, we define algebraic R -vector bundles over an affine real algebraic variety X; the definition requires that an algebraic vector bundle be algebraically isomorphic to a …

In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying …

Jan 31, 2025 · Given a principal bundle pi:A->M, with fiber a Lie group G and base manifold M, and a group representation of G, say phi:G×V->V, then the associated vector bundle is …

In mathematics, the term Riemann–Hilbert correspondence refers to the correspondence between regular singular flat connections on algebraic vector bundles and representations of the …

Let be a scheme over a field (for example, an algebraic variety) with a line bundle . (A line bundle may also be called an invertible sheaf.)Let ,..., be elements of the -vector space (,) of global …

The twisted cubic is a projective algebraic variety.. Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics.Classically, an algebraic variety is …