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...

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...

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

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...

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...

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

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...

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

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...

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...

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...

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

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

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

base, it is called a frustum. An elliptical cone is a cone with an elliptical base. A generalized cone is the surface created by the set of lines passing...

2 = 1 {\displaystyle \varepsilon _{1}=0,\varepsilon _{2}=1} (imaginary elliptic cylinder), and ε 4 = 1 {\displaystyle \varepsilon _{4}=1} (pair of complex...

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...

modular surface is one of the elliptic surfaces studied by Shioda (1972). Barth, Wolf; Hulek, Klaus (1985), "Projective models of Shioda modular surfaces",...

named for Michel Raynaud (1978). To be precise, a Raynaud surface is a quasi-elliptic surface over an algebraic curve of genus g greater than 1, such that...

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

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

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 elliptic geometry, two lines are Clifford parallel or paratactic lines if the perpendicular distance between them is constant from point to point. The...

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...

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 elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the...