affine varieties

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Affine (pronounced /əˈfaɪn/) relates to connections or affinities. It may refer to: *Affine, a in law and anthropology * Affine cipher, a special case of the more general substitution cipher *
Affine combinationIn mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ha ...
, a certain kind of constrained linear combination *
Affine connection In differential geometry Differential geometry is a Mathematics, mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry. The Differentia ...
, a connection on the tangent bundle of a differentiable manifold * Affine Coordinate System, a coordinate system that can be viewed as a Cartesian coordinate system where the axes have been placed so that they are not necessarily orthogonal to each other. See
tensor In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...

. * Affine differential geometry, a geometry that studies differential invariants under the action of the special affine group * Affine gap penalty, the most widely used scoring function used for sequence alignment, especially in bioinformatics *
Affine geometry In mathematics, affine geometry is what remains of Euclidean geometry when not using (mathematicians often say "when forgetting") the metric space, metric notions of distance and angle. As the notion of ''parallel lines'' is one of the main prop ...
, a geometry characterized by parallel lines *
Affine group In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It h ...
, the group of all invertible affine transformations from any affine space over a field ''K'' into itself *
Affine logicAffine logic is a substructural logic In logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit=possessed of reason, intellectual, dialectical, argumentative, translit=logikḗ)Also related to (''logos' ...
, a substructural logic whose proof theory rejects the structural rule of contraction *
Affine representationIn mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ha ...
, a continuous group homomorphism whose values are automorphisms of an affine space *
Affine scheme In commutative algebra Commutative algebra is the branch of algebra Algebra (from ar, الجبر, lit=reunion of broken parts, bonesetting, translit=al-jabr) is one of the areas of mathematics, broad areas of mathematics, together with ...
, the spectrum of prime ideals of a commutative ring **
Affine morphismIn algebraic geometry, a sheaf of algebras on a ringed space ''X'' is a sheaf of commutative rings on ''X'' that is also a sheaf of modules, sheaf of \mathcal_X-modules. It is quasi-coherent sheaf, quasi-coherent if it is so as a module. When ''X'' ...
, a
morphism of schemesIn algebraic geometry, a morphism of schemes generalizes a morphism of algebraic varieties just as a scheme generalizes an algebraic variety Algebraic varieties are the central objects of study in algebraic geometry Algebraic geometry is a b ...
such that the pre-image of an open affine subscheme is affine *Affine space, an abstract structure that generalises the affine-geometric properties of Euclidean space * Affine
tensor In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...

, a tensor belonging to an affine coordinate system *Affine transformation, a transformation that preserves the relation of parallelism between lines