An algebraic manifold, often referred to more generally as an algebraic variety when discussing its structure in algebraic geometry, is a fundamental concept that blends algebra and geometry. Here are the key aspects of algebraic manifolds: 1. **Definition**: An algebraic manifold is typically defined as a set of solutions to a system of polynomial equations. More formally, an algebraic variety is the set of points in a projective or affine space that satisfy these polynomial equations.
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