Ample line bundle information

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...

geometry. For example, the fact that the canonical bundle is a negative multiple of the ample line bundle O ( 1 ) {\displaystyle {\mathcal {O}}(1)} means...

canonical line bundle makes projective spaces prime examples of Fano varieties, equivalently, their anticanonical line bundle is ample (in fact very ample). Their...

there exists a very ample sheaf on X relative to S. Indeed, if X is proper, then an immersion corresponding to the very ample line bundle is necessarily closed...

In algebraic geometry, a Seshadri constant is an invariant of an ample line bundle L at a point P on an algebraic variety. It was introduced by Demailly...

linearizations of the trivial line bundle. See Example 2.16 of [1] for an example of a variety for which most line bundles are not linearizable. Given an...

third power of an ample line bundle is normally generated. The Mumford–Kempf theorem states that the fourth power of an ample line bundle is quadratically...

image D ¯ {\displaystyle {\bar {D}}} is abbreviated with D.) For an ample line bundle H on S, the definition { H } ⊥ := { D ∈ N u m ( S ) | D ⋅ H = 0 }...

K3 surface together with an ample line bundle L such that L is primitive (that is, not 2 or more times another line bundle) and c 1 ( L ) 2 = 2 g − 2 {\displaystyle...

divisorial scheme is a scheme admitting an ample family of line bundles, as opposed to an ample line bundle. In particular, a quasi-projective variety...

the theory of schemes, a related notion is ample line bundle. (For example, if L is an ample line bundle, some power of it is generated by global sections...

zero, L {\displaystyle L} is an ample line bundle on X {\displaystyle X} , and K X {\displaystyle K_{X}} a canonical bundle, then H j ( X , K X ⊗ L ) = 0...

Hilbert polynomial Φ {\displaystyle \Phi } . For a relatively very ample line bundle L ∈ Pic ( X ) {\displaystyle {\mathcal {L}}\in {\text{Pic}}(X)} and...

of more than two polynomials. We can construct it using the very ample line bundle O ( 3 ) {\displaystyle {\mathcal {O}}(3)} over P 1 {\displaystyle...

irreducible representation as the space of global sections of an ample line bundle; the highest weight theorem results as a consequence. (The approach...

complete toric variety that has no non-trivial line bundle; thus, in particular, it has no ample line bundle. Definition 1.1.12 in Ginzburg, V., 1998. Lectures...

Zariski tangent space Function field of an algebraic variety Ample line bundle Ample vector bundle Linear system of divisors Birational geometry Blowing up...