of an ample line bundle, although there are several related classes of line bundles. Roughly speaking, positivity properties of a line bundle are related...

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...

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...

{\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...

anticanonical bundle is the corresponding inverse bundle ω − 1 {\displaystyle \omega ^{-1}} . When the anticanonical bundle of V {\displaystyle V} is ample, V {\displaystyle...

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...

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...

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...

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...

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...