Algebraic geometry

Algebraic geometry studies the shapes and properties of sets of points that satisfy polynomial equations. For example, the set of all points $(x, y)$ that make $y = x^2$ true forms a curve called a parabola. These sets can be curves, surfaces, or more complicated objects, and are called algebraic varieties.

Important properties

• Algebraic geometry connects algebra (polynomials, equations) with geometry (shapes, curves).

• A solution to a polynomial equation in two variables gives a curve in the plane.

• Algebraic varieties can be points, curves, surfaces, or higher-dimensional objects.

• Changing the equation changes the shape of the variety.