noun
algebraic variety
In algebraic geometry, a set of solutions to a system of polynomial equations over an algebraically closed field.
代数多様体は代数幾何学の中心的な研究対象である。
Algebraic varieties are central objects of study in algebraic geometry.
この代数多様体は特異点を持たない。
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'.