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If the Taniyama-Shimura conjecture holds for all semistable elliptic curves, then Fermat's last theorem is true. Before its proof by Ribet in 1986, the theorem had been ...

Associated with an irreducible curve of curve genus p, there are p linearly independent integrals of the first sort. The roots of the integrands are groups of the canonical ...

There is a one-to-one correspondence between the sets of equivalent correspondences (not of value 0) on an irreducible curve of curve genus p, and the rational collineations ...

One of the straight lines sweeping out a ruled surface. The rulings on a ruled surface are asymptotic curves.

If J is a simple closed curve in R^2, the closure of one of the components of R^2-J is homeomorphic with the unit 2-ball. This theorem may be proved using the Riemann mapping ...

Given three curves phi_1, phi_2, phi_3 with the common group of ordinary points G (which may be empty), let their remaining groups of intersections g_(23), g_(31), and g_(12) ...

A surface of revolution is a surface generated by rotating a two-dimensional curve about an axis. The resulting surface therefore always has azimuthal symmetry. Examples of ...

A conjecture which relates the minimal elliptic discriminant of an elliptic curve to the j-conductor. If true, it would imply Fermat's last theorem for sufficiently large ...

Let the speed sigma of a closed curve on the unit sphere S^2 never vanish. Then the tangent indicatrix, also called the tantrix, tau=(sigma^.)/(|sigma^.|) is another closed ...

A surface of revolution obtained by rotating a closed plane curve about an axis parallel to the plane which does not intersect the curve. The simplest toroid is the torus. ...