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...

surfaces, and families thereof, sorted according to their Kodaira dimension following Enriques–Kodaira classification. Projective plane Cone (geometry) Cylinder...

their growth rate, measured by the Kodaira dimension. κ {\displaystyle \kappa } is the Kodaira dimension: it is − ∞ {\displaystyle -\infty } (sometimes...

redirection), follows: Examples of algebraic surfaces include (κ is the Kodaira dimension): κ = −∞: the projective plane, quadrics in P3, cubic surfaces, Veronese...

MR 2343868 Baire set Kodaira vanishing theorem Kodaira–Spencer mapping Kodaira dimension Kodaira surface Kodaira embedding theorem Kodaira's classification...

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...

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...

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...

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...

rational normal curve. The Iitaka dimension of the canonical bundle of a smooth variety is called its Kodaira dimension. Consider on complex algebraic varieties...

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...

2.  The Kodaira dimension of a normal variety X is the Kodaira dimension of its canonical sheaf. Kodaira vanishing theorem See the Kodaira vanishing...

is an elliptic surface (with no singular fibers). All surfaces of Kodaira dimension 1 are elliptic surfaces. Every complex Enriques surface is elliptic...

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...

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...

VII are non-algebraic complex surfaces studied by (Kodaira 1964, 1968) that have Kodaira dimension −∞ and first Betti number 1. Minimal surfaces of class...

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...

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...

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...

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...

one of the classes of surfaces of Kodaira dimension 0 in the Enriques–Kodaira classification. The Kodaira dimension is 0.[clarification needed] Hodge...

simplicity is assumed non-singular. There are two cases based on its Kodaira dimension, κ ( X ) {\displaystyle \kappa (X)} : κ ( X ) = − ∞ . {\displaystyle...

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...

fibrations induced by pluri-canonical systems on varieties of non-negative Kodaira dimension. The problem consists of two halves: one related to general fibres...

singularities Rational variety Unirational variety Ruled variety Kodaira dimension Canonical ring Minimal model program Intersection theory Intersection...

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...

In mathematics, the Kodaira embedding theorem characterises non-singular projective varieties, over the complex numbers, amongst compact Kähler manifolds...

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...

"Autoequivalences of derived categories of elliptic surfaces with non-zero Kodaira dimension". pp. 10–12. arXiv:1501.06657 [math.AG]. Stability conditions on A...

is birationally equivalent to a modular Calabi–Yau manifold with Kodaira dimension zero. Siegel modular varieties cannot be anabelian. Siegel modular...