the canonical bundle of a non-singular algebraic variety V {\displaystyle V} of dimension n {\displaystyle n} over a field is the line bundle Ω n =...

of canonical coordinates in classical mechanics may be generalized to a more abstract 20th century definition of coordinates on the cotangent bundle of...

) {\displaystyle R(V,K)=R(V,K_{V})\,} of sections of powers of the canonical bundle K. Its nth graded component (for n ≥ 0 {\displaystyle n\geq 0} ) is:...

also tautological bundles on a projective bundle of a vector bundle as well as a Grassmann bundle. The older term canonical bundle has dropped out of...

the canonical bundle in the ordinary case. It is sometimes also called the pure spinor bundle, as its sections are pure spinors. The canonical bundle is...

compute the canonical bundle of a minimal elliptic surface f: X → S. Over the complex numbers, Kodaira proved the following canonical bundle formula: K...

denoted h 0 ( X , L ) {\displaystyle h^{0}(X,L)} . Let K denote the canonical bundle on X. Then, the Riemann–Roch theorem states that h 0 ( X , L ) − h...

:TM\rightarrow M} is the canonical projection. Pushforward (differential) Unit tangent bundle Cotangent bundle Frame bundle Musical isomorphism The disjoint...

power of the canonical bundle of M {\displaystyle M} is trivial. M {\displaystyle M} has a finite cover that has trivial canonical bundle. M {\displaystyle...

element of a set partition Canonical one-form, a special 1-form defined on the cotangent bundle T*M of a manifold M Canonical symplectic form, the exterior...