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

vector bundle is a (holomorphic or algebraic) vector bundle that is stable in the sense of geometric invariant theory. Any holomorphic vector bundle may...

important line bundles in algebraic geometry is the tautological line bundle on projective space. The projectivization P(V) of a vector space V over a...

line bundles and a generalization of the theorem to algebraic curves. The theorem will be illustrated by picking a point P {\displaystyle P} on the surface...

In mathematics, a distinctive feature of algebraic geometry is that some line bundles on a projective variety can be considered "positive", while others...

Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as...

Exterior algebras of vector bundles are frequently considered in geometry and topology. There are no essential differences between the algebraic properties...

concepts such as locally free modules, the algebraic counterpart to vector bundles. Roughly, affine spaces are vector spaces whose origins are not specified...

vector bundles, the Levi-Civita connection on the tangent bundle of a pseudo-Riemannian manifold, which gives a standard way to differentiate vector fields...

In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent...