of an ample line bundle, although there are several related classes of line bundles. Roughly speaking, positivity properties of a line bundle are related...
39 KB (6,685 words) - 15:21, 4 June 2024
a bundle to have no non-zero global sections at all; this is the case for the tautological line bundle. When the line bundle is sufficiently ample this...
11 KB (1,612 words) - 01:22, 27 April 2024
called semi-ample if some positive tensor power L ⊗ a {\displaystyle L^{\otimes a}} is basepoint-free. It follows that a semi-ample line bundle is nef. Semi-ample...
13 KB (2,037 words) - 18:59, 9 December 2023
Moduli space (redirect from Moduli of vector bundles)
{\displaystyle i^{*}x_{0},\ldots ,i^{*}x_{n}} . Conversely, given an ample line bundle L → X {\displaystyle {\mathcal {L}}\to X} globally generated by n...
28 KB (4,048 words) - 18:33, 6 February 2024
anticanonical bundle is the corresponding inverse bundle ω − 1 {\displaystyle \omega ^{-1}} . When the anticanonical bundle of V {\displaystyle V} is ample, V {\displaystyle...
16 KB (2,529 words) - 19:58, 22 July 2024
interpretation of the ample line bundle over the moduli space of vector bundles on a compact Riemann surface, known as the Quillen determinant line bundle. It can be...
13 KB (2,063 words) - 13:52, 24 June 2023
tautological bundle is known as the tautological line bundle. The tautological bundle is also called the universal bundle since any vector bundle (over a compact...
14 KB (2,441 words) - 11:51, 28 December 2023
Positive form (section Positive line bundles)
Kodaira embedding theorem claims that a positive line bundle is ample, and conversely, any ample line bundle admits a Hermitian metric with − 1 Θ {\displaystyle...
5 KB (719 words) - 14:35, 29 June 2024
Iitaka dimension (redirect from Big line bundle)
varieties, and if L is a big line bundle on X, then f*L is a big line bundle on Y. All ample line bundles are big. Big line bundles need not determine birational...
7 KB (1,128 words) - 18:16, 27 September 2023
Appell–Humbert theorem (section Ample line bundles)
Lefschetz proved that the line bundle L {\displaystyle L} , associated to the Hermitian form H {\displaystyle H} is ample if and only if H {\displaystyle...
5 KB (730 words) - 08:06, 21 August 2024