Hyperelliptic curve

Summary

A hyperelliptic curve is a smooth projective algebraic curve of genus at least $2$ that is a double cover of the projective line. Away from characteristic $2$, it has an affine model $y^2 = f(x)$ with $f$ a squarefree polynomial. Hyperelliptic curves are the simplest curves of higher genus. They are the exceptions in many results, such as Clifford's theorem and the embedding by the canonical divisor.