algebraic variety

Noun

algebraic variety (plural algebraic varieties)

1. The set of solutions of a given system of polynomial equations over the real or complex numbers; any of certain generalisations of such a set that preserves the geometric intuition implicit in the original definition.
   • If #92;mathcal#123;W#125; is a locally closed subset (i.e., the intersection of open and closed sets) of an algebraic variety, it becomes an algebraic variety in a natural manner since the germs of regular functions at x#92;in#92;mathcal#123;W#125; axe taken to be the germs of functions on...2005, Giovanni Giachetta, Luigi Mangiarotti, Gennadi Sardanashvili, Geometric and Algebraic Topological Methods in Quantum Mechanics, World Scientific, page 87
   • The quest for understanding the structure of algebraic varieties is a very natural one.[…]A landmark from that time was Hironaka's 1964 theorem on the existence of a smooth model for any complex algebraic variety.2011, Carel Faber, Gerard van der Geer, Eduard Looijenga, Classification of Algebraic Varieties, European Mathematical Society, page vii

   Synonyms:

   variety