Live briefing
Everything about Stable vector bundle
In mathematics, a stable vector bundle is a vector bundle that is stable in the sense of geometric invariant theory. Any holomorphic vector bundle may be built from stable ones using Harder–Narasimhan filtration. Stable bundles were defined by David Mumford in Mumford (1963) and later built upon by David Gieseker, Fedor Bogomolov, Thomas Bridgeland and many others. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Stable vector bundleA 5-minute orientation
- Skim a recent paper: Genuinely ramified maps and stable vector bundlesInfluential work since 2022
- Pick up a classic book: Lectures on Riemann surfacesThe most-reprinted book on the subject
- Read the landmark paper: An elliptic conic bundle in $\mathbb{P}^4$ arising from a stable rank-3 vector bundleCited 25 times
- Go sideways: Bridgeland stability conditionA closely related topic
- Go sideways: Kobayashi–Hitchin correspondenceA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
An elliptic conic bundle in $\mathbb{P}^4$ arising from a stable rank-3 vector bundle
On the spectrum of a stable rank 2 vector bundle on ℙ 3
Stability of Picard bundle over moduli space of stable vector bundles of rank two over a curve
Constructing stable vector bundles from curves with torsion normal bundle
The order and the characteristic classes of a stable vector bundle
🆕 Influential since 2022
📚 Books worth reading
Lectures on Riemann surfacesCollege on Riemann Surfaces (1st 1987 International Centre for Theoretical Physics) · 1989
Scale Space and Variational Methods in Computer VisionArjan Kuijper · 2013- 📕Stable vector-bundles over non-Kählerian surfacesAndrei-Dumitru Teleman · 1993
- 📕The moduli space of stable vector bundles on a punctured Riemann surfaceJonathan Adam Poritz · 1992
- 📕Riemanniam metrics of non-negative curvature on stable vector bundles over spheresAlcibiades Rigas · 1974
- 📕The construction of stable vector bundle on surface of low second Chern classJun Li · 1989
- 📕Positivity of the curvature of the Weil-Petersson metric on the moduli space of stable vector bundlesKoji Cho · 1985
- 📕Moduli spaces of stable rank two vector bundles and computations of Donaldson polynomials over rational ruled surfacesWeiping Li · 1991
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Bridgeland stability condition In mathematics, and especially algebraic geometry, a Bridgeland stability condition is an algebro-geometric stability condition defined on elements of…
- Kobayashi–Hitchin correspondence In differential geometry, algebraic geometry, and gauge theory, the Kobayashi–Hitchin correspondence (or Donaldson–Uhlenbeck–Yau theorem) relates stable…
- Lange's conjecture In algebraic geometry, Lange's conjecture is a theorem about stability of vector bundles over curves, introduced by Herbet Lange [de] and proved by Montserrat…
- Coherent sheaf In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric…
- K-stability of Fano varieties In mathematics, and in particular algebraic geometry, K-stability is an algebro-geometric stability condition for projective algebraic varieties and complex…
- Convexity (algebraic geometry) In algebraic geometry, convexity is a restrictive technical condition for algebraic varieties originally introduced to analyze Kontsevich moduli spaces…
- Gauge theory (mathematics) In mathematics, and especially differential geometry and mathematical physics, gauge theory is the general study of connections on vector bundles, principal…
- Glossary of algebraic geometry This is a glossary of algebraic geometry. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory…