algebraic variety
In algebraic geometry, a set of solutions to a system of polynomial equations over an algebraically closed field.
Algebraic varieties are central objects of study in algebraic geometry.
This algebraic variety has no singular points.
代数幾何学 is the field of algebraic geometry, while 代数多様体 refers to the geometric objects studied within that field.
Compound of 代数 (algebra) and 多様体 (manifold), calque of English 'algebraic variety'.