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Tom Thistlethwaite Tom Thistlethwaite

October 7 at 5:35 AM ·

Hyperelliptic Curve

A hyperelliptic curve is an algebraic curve given by an equation of the form y^2=f(x), where f(x) is a polynomial of degree n>4 with n distinct roots.

If f(x) is a cubic or quartic polynomial, then the curve is called an elliptic curve.

The genus of a hyperelliptic curve is related to the degree of the polynomial. A polynomial of degree 2g+1 or 2g+2 gives a curve of genus g. All curves of genus 2 are hyperelliptic, but for larger genus there are curves that are not hyperelliptic.

DEMONSTRATIONS.WOLFRAM.COM

Hopf Fibration of the Three-Sphere - Wolfram Demonstrations Project

The Hopf fibration is a fibration of into fibers diffeomorphic to the quotient space is In other words the sphere can be used to parametrize the fibers of the Hopf fibration is projected into via stereographic projection and each fiber intersects the top half of the unit sphere only once except for....

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