In algebraic geometry, the Kodaira dimension κ(X) measures the size of the canonical model of a projective variety X. Igor Shafarevich in a seminar introduced...
20 KB (2,402 words) - 02:25, 9 June 2024
surfaces, and families thereof, sorted according to their Kodaira dimension following Enriques–Kodaira classification. Projective plane Cone (geometry) Cylinder...
7 KB (828 words) - 18:38, 4 February 2024
their growth rate, measured by the Kodaira dimension. κ {\displaystyle \kappa } is the Kodaira dimension: it is − ∞ {\displaystyle -\infty } (sometimes...
31 KB (4,245 words) - 12:01, 28 February 2024
redirection), follows: Examples of algebraic surfaces include (κ is the Kodaira dimension): κ = −∞: the projective plane, quadrics in P3, cubic surfaces, Veronese...
7 KB (973 words) - 18:40, 4 February 2024
MR 2343868 Baire set Kodaira vanishing theorem Kodaira–Spencer mapping Kodaira dimension Kodaira surface Kodaira embedding theorem Kodaira's classification...
10 KB (946 words) - 18:33, 9 August 2024
Birational geometry (section Kodaira dimension)
the Kodaira dimension, which measures the growth of the plurigenera Pd as d goes to infinity. The Kodaira dimension divides all varieties of dimension n...
20 KB (2,684 words) - 22:32, 2 January 2024
the Kodaira dimension of V. One can define an analogous ring for any line bundle L over V; the analogous dimension is called the Iitaka dimension. A line...
4 KB (464 words) - 18:26, 21 May 2023
In the Enriques–Kodaira classification of surfaces, K3 surfaces form one of the four classes of minimal surfaces of Kodaira dimension zero. A simple example...
34 KB (5,241 words) - 11:22, 18 August 2023
their Kodaira dimension, as in the complex case. The four classes are: a) Kodaira dimension minus infinity. These are the ruled surfaces. b) Kodaira dimension...
20 KB (2,067 words) - 01:32, 19 August 2024
rational normal curve. The Iitaka dimension of the canonical bundle of a smooth variety is called its Kodaira dimension. Consider on complex algebraic varieties...
7 KB (1,128 words) - 18:16, 27 September 2023
algebraic surface with Kodaira dimension 2. Because of Chow's theorem any compact complex manifold of dimension 2 and with Kodaira dimension 2 will actually...
9 KB (1,446 words) - 18:06, 13 July 2024
Glossary of algebraic geometry (redirect from Pure dimension)
2. The Kodaira dimension of a normal variety X is the Kodaira dimension of its canonical sheaf. Kodaira vanishing theorem See the Kodaira vanishing...
82 KB (12,488 words) - 04:04, 4 August 2024
is an elliptic surface (with no singular fibers). All surfaces of Kodaira dimension 1 are elliptic surfaces. Every complex Enriques surface is elliptic...
16 KB (1,883 words) - 18:07, 26 July 2024
theorem. The statement of Kunihiko Kodaira's result is that if M is a compact Kähler manifold of complex dimension n, L any holomorphic line bundle on...
7 KB (846 words) - 19:33, 26 April 2024
non-singular. An elliptic curve is an abelian variety of dimension 1. Abelian varieties have Kodaira dimension 0. In the early nineteenth century, the theory of...
21 KB (2,918 words) - 10:20, 25 April 2024
VII are non-algebraic complex surfaces studied by (Kodaira 1964, 1968) that have Kodaira dimension −∞ and first Betti number 1. Minimal surfaces of class...
7 KB (892 words) - 13:39, 25 May 2024
characteristic zero has Kodaira dimension −∞. The converse is a conjecture which is known in dimension at most 3: a variety of Kodaira dimension −∞ over a field...
7 KB (817 words) - 10:18, 24 January 2023
Divisor (algebraic geometry) (section Kodaira's lemma)
H0(X, mKX) (meaning H0(X, O(mKX))) as m increases. The Kodaira dimension divides all n-dimensional varieties into n+2 classes, which (very roughly) go from...
40 KB (6,609 words) - 18:59, 14 April 2023
polynomial equations than others. This is formalized by the notion of Kodaira dimension of a variety, and by this measure projective spaces are the most special...
10 KB (1,469 words) - 01:13, 5 May 2024
mathematics, a Kodaira surface is a compact complex surface of Kodaira dimension 0 and odd first Betti number. The concept is named after Kunihiko Kodaira. These...
3 KB (355 words) - 12:09, 8 November 2023
one of the classes of surfaces of Kodaira dimension 0 in the Enriques–Kodaira classification. The Kodaira dimension is 0.[clarification needed] Hodge...
4 KB (397 words) - 21:40, 7 September 2024
simplicity is assumed non-singular. There are two cases based on its Kodaira dimension, κ ( X ) {\displaystyle \kappa (X)} : κ ( X ) = − ∞ . {\displaystyle...
10 KB (1,351 words) - 11:54, 26 July 2023
they are not unirational. They accomplished this by studying the Kodaira dimension of the coarse moduli spaces κ g = K o d ( M ¯ g ) , {\displaystyle...
24 KB (3,665 words) - 06:51, 6 June 2024
fibrations induced by pluri-canonical systems on varieties of non-negative Kodaira dimension. The problem consists of two halves: one related to general fibres...
16 KB (1,247 words) - 14:30, 23 August 2024
singularities Rational variety Unirational variety Ruled variety Kodaira dimension Canonical ring Minimal model program Intersection theory Intersection...
7 KB (600 words) - 19:55, 10 January 2024
Projective variety (section Kodaira vanishing)
canonical ring or model can then be used to define the Kodaira dimension of X. Projective schemes of dimension one are called projective curves. Much of the theory...
45 KB (7,530 words) - 18:38, 11 December 2022
In mathematics, the Kodaira embedding theorem characterises non-singular projective varieties, over the complex numbers, amongst compact Kähler manifolds...
4 KB (408 words) - 12:26, 27 August 2024
variety is finitely generated. The Kodaira dimension of V is the dimension of the canonical ring minus one. Here the dimension of the canonical ring may be...
16 KB (2,529 words) - 19:58, 22 July 2024
"Autoequivalences of derived categories of elliptic surfaces with non-zero Kodaira dimension". pp. 10–12. arXiv:1501.06657 [math.AG]. Stability conditions on A...
6 KB (993 words) - 14:29, 3 September 2024
is birationally equivalent to a modular Calabi–Yau manifold with Kodaira dimension zero. Siegel modular varieties cannot be anabelian. Siegel modular...
12 KB (1,147 words) - 00:25, 17 July 2024