projective variety defined by this graded ring is called the canonical model of V, and the dimension of the canonical model is called the Kodaira dimension...

In mathematics, the canonical bundle of a non-singular algebraic variety V {\displaystyle V} of dimension n {\displaystyle n} over a field is the line...

K_{X}^{d}))=\mathbf {P} ^{P_{d}-1},} called the d-canonical map. The canonical ring R(KX) of a variety X is the graded ring R ( K X ) := ⨁ d ≥ 0 H 0 ( X , K X d )...

average of its vertices Canonical ring, a graded ring associated to an algebraic variety Canonical injection, in set theory Canonical representative, in set...

in the minimal model program, given by blowing up along a relative canonical ring. In dimension 3 flips are used to construct minimal models, and any...

\end{aligned}}} for all a, b in R. The ring R / I is also called a factor ring. As with a quotient group, there is a canonical homomorphism p : R → R / I, given...

by g. If I is an ideal of a ring R, then there is a canonical surjective ring homomorphism from R onto the quotient ring R / I, that sends an element...

the canonical ring of X. If the canonical ring is finitely generated, then Proj of the ring is called the canonical model of X. The canonical ring or model...

Canonical model may refer to: Canonical model, a design pattern used to communicate between different data formats Canonical ring in mathematics Kripke...

canonical ring of a normal variety X is the section ring of the canonical sheaf. canonical model The canonical model is the Proj of a canonical ring (assuming...

correspondence between the ring of modular forms of Γ and a particular section ring closely related to the canonical ring of a stacky curve. There is...

multiplicative set in a commutative ring R, and j : R → S − 1 R {\displaystyle j\colon R\to S^{-1}R} be the canonical ring homomorphism. Given an ideal I in...

dualizing module, also called a canonical module, is a module over a commutative ring that is analogous to the canonical bundle of a smooth variety. It...

Ruled variety Kodaira dimension Canonical ring Minimal model program Intersection theory Intersection number Chow ring Chern class Serre's multiplicity...

provides two such notions, canonical equivalence and compatibility. Code point sequences that are defined as canonically equivalent are assumed to have...

each such pair, we can apply the ring homomorphism φ to the factorization of a+bα, and we can apply the canonical ring homomorphism from Z to Z/nZ to the...

In the practice of Christianity, canonical hours mark the divisions of the day in terms of fixed times of prayer at regular intervals. A book of hours...

enumerative geometry. Voight, John; Zureick-Brown, David (2015). The canonical ring of a stacky curve. Memoirs of the American Mathematical Society. arXiv:1501...

A canonical coronation (Latin: Coronatio Canonica) is a pious institutional act of the pope, duly expressed in a formal decree of a papal bull, in which...

In mathematics, a canonical basis is a basis of an algebraic structure that is canonical in a sense that depends on the precise context: In a coordinate...

context of graded rings R, the canonical module of a Gorenstein ring R is isomorphic to R with some degree shift. For a Gorenstein local ring (R, m, k) of...

endomorphisms under the above operations is a canonical example of a near-ring that is not a ring. Endomorphism rings always have additive and multiplicative...

Canonical basis Canonical form Frobenius normal form Jordan matrix Jordan–Chevalley decomposition Matrix decomposition Modal matrix Weyr canonical form...

also proved several other problems including finite generation of log canonical rings and existence of minimal models for varieties of log general type....

Non-Vanishing Theorem and an Analytic Proof of the Finite Generation of the Canonical Ring". arXiv:math.AG/0610740. "Stefan Bergman Prize". American Mathematical...

M∗ or HomR(M, R). If the base ring R is a field, then a dual module is a dual vector space. Every module has a canonical homomorphism to the dual of its...

may also be referred to as an inclusion function, an insertion, or a canonical injection. A "hooked arrow" (U+21AA ↪ RIGHTWARDS ARROW WITH HOOK) is sometimes...

two rings cannot be aromatic and so will accept the nonstandard form c1ccccc1c2ccccc2.) The Daylight and OpenEye algorithms for generating canonical SMILES...

algebraic geometry, in particular his proof of the finite generation of the canonical ring, the existence of flips and the boundedness of varieties of log general...

conjectures including existence of log flips, finite generation of log canonical rings, and existence of minimal models for varieties of log general type...