## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

### *2.10. Affine and Projective Curves

In this section, we introduce some elementary concepts from algebraic geometry, which facilitate the treatment of elliptic and hyperelliptic curves in the next two sections. We concentrate only on plane curves, because these are the only curves we need in this book. Throughout this section, K denotes a field (finite or infinite) and the algebraic closure of K.

#### 2.10.1. Plane Curves

The solutions of a polynomial equation f(X, Y) = 0 is one of the central objects of study in algebraic geometry. For example, we know that in the equation X2 + Y2 – 1 = 0 represents a circle with origin at (0, 0) and with radius ...

## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required