In algebraic geometry, divisors are a generalization of codimension-1 subvarieties of algebraic varieties. Two different generalizations are in common...

In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of curves; the dimension of the...

divides evenly another integer Divisor (ring theory), a generalization of the preceding concept Divisor (algebraic geometry), a generalization of codimension...

This is a glossary of algebraic geometry. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory...

geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry...

important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic...

one, and G {\displaystyle G} be a divisor with disjoint support from D {\displaystyle D} . The algebraic geometry code C L ( D , G ) {\displaystyle C_{\mathcal...

special divisors is a result of William K. Clifford (1878) on algebraic curves, showing the constraints on special linear systems on a curve C. A divisor on...

mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has...

integrally closed). In algebraic geometry, normal crossing divisors are a class of divisors which generalize the smooth divisors. Intuitively they cross...

In algebraic geometry, given a pair (X, D) consisting of a normal variety X and a Q {\displaystyle \mathbb {Q} } -divisor D on X (e.g., canonical divisor)...

arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around...

Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as...

In algebraic geometry, the function field of an algebraic variety V consists of objects that are interpreted as rational functions on V. In classical algebraic...

version of the construction of the divisor class group, or ideal class group, and is much used in algebraic geometry and the theory of complex manifolds...

In algebraic geometry, a line bundle on a projective variety is nef if it has nonnegative degree on every curve in the variety. The classes of nef line...

V {\displaystyle V} , and any divisor in it may be called a canonical divisor. An anticanonical divisor is any divisor − K {\displaystyle K} with K {\displaystyle...

space plays a central role in algebraic geometry. This article aims to define the notion in terms of abstract algebraic geometry and to describe some basic...

In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in...

In mathematics, specifically algebraic geometry, an exceptional divisor for a regular map f : X → Y {\displaystyle f:X\rightarrow Y} of varieties is a...

optimizing departure times for a network of trains. Tropical geometry is a variant of algebraic geometry in which polynomial graphs resemble piecewise linear...

In algebraic geometry, motives (or sometimes motifs, following French usage) is a theory proposed by Alexander Grothendieck in the 1960s to unify the vast...

the Hodge index theorem for an algebraic surface V determines the signature of the intersection pairing on the algebraic curves C on V. It says, roughly...

called divisors. The earliest work on algebraic cycles focused on the case of divisors, particularly divisors on algebraic curves. Divisors on algebraic curves...

transcendental methods to algebraic geometry falls in this category, together with more geometric aspects of complex analysis. Complex geometry sits at the intersection...

Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields...

and Lazarsfeld (2009). In algebraic geometry, the multiplier ideal of an effective Q {\displaystyle \mathbb {Q} } -divisor measures singularities coming...

In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric...

In mathematics, the theta divisor Θ is the divisor in the sense of algebraic geometry defined on an abelian variety A over the complex numbers (and principally...

In mathematics, a distinctive feature of algebraic geometry is that some line bundles on a projective variety can be considered "positive", while others...