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

In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space...

algebraic geometry, a stable principal bundle is a generalisation of the notion of a stable vector bundle to the setting of principal bundles. The concept of...

information. Coherent sheaves can be seen as a generalization of vector bundles. Unlike vector bundles, they form an abelian category, and so they are closed under...

Narasimhan–Seshadri theorem which defines a correspondence between stable vector bundles and unitary representations of the fundamental group of a compact...

In mathematics, a Higgs bundle is a pair ( E , φ ) {\displaystyle (E,\varphi )} consisting of a holomorphic vector bundle E and a Higgs field φ {\displaystyle...

Donaldson–Uhlenbeck–Yau theorem) relates stable vector bundles over a complex manifold to Einstein–Hermitian vector bundles. The correspondence is named after...

a branch of mathematics, the stable normal bundle of a differentiable manifold is an invariant which encodes the stable normal (dually, tangential) data...

Narasimhan and Seshadri (1965), says that a holomorphic vector bundle over a Riemann surface is stable if and only if it comes from an irreducible projective...

gauge theory is the general study of connections on vector bundles, principal bundles, and fibre bundles. Gauge theory in mathematics should not be confused...

the group PGL5g–5. Example: A vector bundle W over an algebraic curve (or over a Riemann surface) is a stable vector bundle if and only if deg ⁡ ( V ) rank...

tangent bundle of a differentiable manifold M {\displaystyle M} is a manifold T M {\displaystyle TM} which assembles all the tangent vectors in M {\displaystyle...

objects, but the stacky version remembers automorphisms of vector bundles. For any stable vector bundle E {\displaystyle E} the automorphism group A u t ( E...

projective bundle is of the form P ( E ) {\displaystyle \mathbb {P} (E)} for some vector bundle (locally free sheaf) E. Every vector bundle over a variety...

a field of mathematics, a normal bundle is a particular kind of vector bundle, complementary to the tangent bundle, and coming from an embedding (or...

clutching construction, homotopy groups of the stable space O are identified with stable vector bundles on spheres (up to isomorphism), with a dimension...

Narasimhan–Seshadri theorem which proved the necessary conditions for stable vector bundles on a Riemann surface. He was a recipient of the Padma Bhushan, India's...

classes of stable vector bundles of rank n {\displaystyle n} and degree d {\displaystyle d} as an open subset. Since a line bundle is stable, such a moduli...

Narasimhan–Seshadri theorem which proved the necessary conditions for stable vector bundles on a Riemann surface.He also introduced and named the concept called...

Hodge bundle The Hodge bundle on the moduli space of curves (of fixed genus) is roughly a vector bundle whose fiber over a curve C is the vector space...

topology and differential topology is a topological space associated to a vector bundle, over any paracompact space. One way to construct this space is as follows...

_{\mathcal {F}}(\lambda )=n\lambda +d+n(1-g)} Then, the locus of semi-stable vector bundles is contained in Q u o t O C ⊕ N / C / Z Φ F , L {\displaystyle {\mathcal...

physics, the number of moduli of vector bundles and the closely related problem of the number of moduli of principal G-bundles has been found to be significant...

especially the Kobayashi–Hitchin correspondence relating slope stable vector bundles to Hermitian Yang–Mills metrics. The conjecture is intimately related...

_{M_{B}^{4k}}\rightarrow \xi } is a bundle map from the stable normal bundle of the Milnor manifold to a certain stable vector bundle. A crucial theorem for the...

of the normal bundle, and also for an abstract (that is, non-embedded) manifold with a given stable trivialisation of the tangent bundle. A related notion...

moduli space of curves. Using the notion of stable vector bundle, coarse moduli schemes for the vector bundles on any smooth complex variety have been shown...

and only if the Spivak normal fibration of X has a reduction to a stable vector bundle. If normal maps of degree one to X exist, their bordism classes (called...

algebraic geometry, Lange's conjecture is a theorem about stability of vector bundles over curves, introduced by Herbet Lange [de] and proved by Montserrat...

S. Narasimhan described the cohomology of the moduli spaces of stable vector bundles over Riemann surfaces by counting the number of points of the moduli...