A regular map between affine spaces over an algebraically closed field is merely one given by polynomials. That is, there are polynomials in variables such that the map is given by where stands for the many components .
A regular map between affine varieties is one which is the restriction of a regular map between affine spaces. That is, if and , then there is a regular map with and . So, this is a map given by polynomials, whose image lies in the intended target.
A regular map between algebraic varieties is a locally regular map. That is is regular if around each point there is an affine variety and around each point there is an affine variety with and such that the restriction is a regular map of affine varieties.
|Date of creation||2013-03-22 12:04:00|
|Last modified on||2013-03-22 12:04:00|
|Last modified by||nerdy2 (62)|