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The number of coincidences of a (nu,nu^') correspondence of value gamma on a curve of curve genus p is given by nu+nu^'+2pgamma.

The dimension of a special series can never exceed half its order.

One of the Plücker characteristics, defined by p=1/2(n-1)(n-2)-(delta+kappa)=1/2(m-1)(m-2)-(tau+iota), where m is the class, n the order, delta the number of nodes, kappa the ...

A cusp is a point at which two branches of a curve meet such that the tangents of each branch are equal. The above plot shows the semicubical parabola curve x^3-y^2=0, which ...

In two dimensions, the curve known as an "egg' is an oval with one end more pointed than the other.

The conjecture that Frey's elliptic curve was not modular. The conjecture was quickly proved by Ribet (Ribet's theorem) in 1986, and was an important step in the proof of ...

A curvature of a submanifold of a manifold which depends on its particular embedding. Examples of extrinsic curvature include the curvature and torsion of curves in ...

The only whole number solution to the Diophantine equation y^3=x^2+2 is y=3, x=+/-5. This theorem was offered as a problem by Fermat, who suppressed his own proof.

H=|aa^'a^('')|a_(x^(n-2))a_(x^(n-2))^'a_(x^(n-2))^('')=0. The nonsingular inflections of a curve are its nonsingular intersections with the Hessian.

Every modular system has a modular system basis consisting of a finite number of polynomials. Stated another way, for every order n there exists a nonsingular curve with the ...