morphisms between affine schemes are of this type and gluing such morphisms gives a morphism of schemes in general. Now, if X, Y are affine varieties;...

R. Projective morphisms are proper, but not all proper morphisms are projective. For example, there is a smooth proper complex variety of dimension 3...

keep track of morphisms between points (i.e., morphisms between morphisms). A rational map of schemes is defined in the same way for varieties. Thus, a rational...

an abelian variety. This association is a duality in the sense that it is contravariant functorial, i.e., it associates to all morphisms f : A → B {\displaystyle...

notable for their color polymorphism and primarily display two color morph varieties ("red-backed" and "lead-backed"), which differ in physiology and anti-predator...

In botanical nomenclature, variety (abbreviated var.; in Latin: varietas) is a taxonomic rank below that of species and subspecies, but above that of...

geometry, a complete algebraic variety is an algebraic variety X, such that for any variety Y the projection morphism X × Y → Y {\displaystyle X\times...

stable under base change and composition. A smooth morphism is universally locally acyclic. Smooth morphisms are supposed to geometrically correspond to smooth...

theory, an algebraic variety over a field is an integral (irreducible and reduced) scheme over that field whose structure morphism is separated and of...

has property P. For example, flat morphisms, smooth morphisms, proper morphisms, and many other classes of morphisms are preserved under arbitrary base...