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 =...
16 KB (2,529 words) - 19:58, 22 July 2024
of canonical coordinates in classical mechanics may be generalized to a more abstract 20th century definition of coordinates on the cotangent bundle of...
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) {\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:...
4 KB (464 words) - 18:26, 21 May 2023
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...
20 KB (3,145 words) - 15:37, 16 February 2024
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...
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Elliptic surface (section Canonical bundle formula)
compute the canonical bundle of a minimal elliptic surface f: X → S. Over the complex numbers, Kodaira proved the following canonical bundle formula: K...
16 KB (1,883 words) - 18:07, 26 July 2024
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...
32 KB (4,966 words) - 14:27, 17 December 2023
:TM\rightarrow M} is the canonical projection. Pushforward (differential) Unit tangent bundle Cotangent bundle Frame bundle Musical isomorphism The disjoint...
17 KB (2,946 words) - 00:48, 7 December 2023
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...
24 KB (3,269 words) - 15:29, 27 September 2024
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...
5 KB (602 words) - 10:15, 4 August 2023