In mathematics, an elliptic surface is a surface that has an elliptic fibration, in other words a proper morphism with connected fibers to an algebraic...

Weierstrass elliptic function. Likewise, genus g surfaces have Riemann surface structures, as (compactifications of) hyperelliptic surfaces y2 = Q(x),...

hyperelliptic surface, or bi-elliptic surface, is a minimal surface whose Albanese morphism is an elliptic fibration without singular fibres. Any such surface can...

provides a basis (up to torsion) for the Mordell–Weil group of an elliptic surface E → S, where S is isomorphic to the projective line. The algorithm...

mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined...

plane). A paraboloid is either elliptic or hyperbolic. Equivalently, a paraboloid may be defined as a quadric surface that is not a cylinder, and has...

hyperbola is called an elliptic cylinder, parabolic cylinder and hyperbolic cylinder, respectively. These are degenerate quadric surfaces. When the principal...

surfaces, all hyperelliptic surfaces, all Kodaira surfaces, some K3 surfaces, some abelian surfaces, and some rational surfaces are elliptic surfaces...

In algebraic geometry, an elliptic singularity of a surface, introduced by Philip Wagreich in 1970, is a surface singularity such that the arithmetic genus...

provides a basis (up to torsion) for the Mordell–Weil group of an elliptic surface E → S {\displaystyle E\to S} , where S {\displaystyle S} is isomorphic...

general elliptic K3 surface has exactly 24 singular fibers, each of type I 1 {\displaystyle I_{1}} (a nodal cubic curve). Whether a K3 surface is elliptic can...

algebraic surfaces Ruled surface Cubic surface Veronese surface Del Pezzo surface Rational surface Enriques surface K3 surface Hodge index theorem Elliptic surface...

1 (an abelian surface) has Kodaira dimension 0; the product of a curve of genus 1 with a curve of genus at least 2 (an elliptic surface) has Kodaira dimension...

A genus one orientable surface is the ordinary torus. A non-orientable surface of genus one is the projective plane. Elliptic curves over the complex...

hyperbolic paraboloid shape. Saddle surfaces have negative Gaussian curvature which distinguish them from convex/elliptical surfaces which have positive Gaussian...

lateral conic surface, a quadric called conical quadric or quadratic cone. In a three-dimensional Cartesian coordinate system, an elliptic cone is the locus...

applied to the Riemann surface of X {\displaystyle X} (its manifold of complex points). For example, the definition of elliptic curve from algebraic geometry...

Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel...

trivial square. Enriques surfaces are all projective (and therefore Kähler over the complex numbers) and are elliptic surfaces of genus 0. Over fields...

second is the possibility of obtaining quasi-elliptic surfaces in characteristics two and three. These are surfaces fibred over a curve where the general fibre...

In mathematics, an abelian surface is a 2-dimensional abelian variety. One-dimensional complex tori are just elliptic curves and are all algebraic, but...

Elliptic surface (Proctor 1993) (Proctor 1993, p. 940) Cameron P.J.; Goethals, J.M.; Seidel, J.J; Shult, E. E. Line graphs, root systems and elliptic...

Amherst College. He studies, among other things, étale homotopy theory, elliptic surfaces, computer-based algebraic geometry (such as Gröbner basis), Torelli...

In astrodynamics or celestial mechanics, an elliptical orbit or eccentric orbit is an orbit with an eccentricity of less than 1; this includes the special...

hyperelliptic surfaces κ = 1: elliptic surfaces κ = 2: surfaces of general type. For more examples see the list of algebraic surfaces. The first five examples...

that every Riemann surface admits a Riemannian metric of constant curvature, where the curvature can be taken to be 1 in the elliptic, 0 in the parabolic...

In mathematics, Dolgachev surfaces are certain simply connected elliptic surfaces, introduced by Igor Dolgachev (1981). They can be used to give examples...

laminated or carriage spring, and sometimes referred to as a semi-elliptical spring, elliptical spring, or cart spring, it is one of the oldest forms of vehicle...

1-dimensional global fields to 2-dimensional arithmetic surfaces such as proper regular models of elliptic curves over global fields. His theory led to three...

point not on the plane of C {\displaystyle C} , one obtains an elliptic cone. A conical surface S {\displaystyle S} can be described parametrically as S (...