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...
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Weierstrass elliptic function. Likewise, genus g surfaces have Riemann surface structures, as (compactifications of) hyperelliptic surfaces y2 = Q(x),...
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hyperelliptic surface, or bi-elliptic surface, is a minimal surface whose Albanese morphism is an elliptic fibration without singular fibres. Any such surface can...
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Cox–Zucker machine (category Algebraic surfaces)
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...
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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...
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Paraboloid (redirect from Elliptic paraboloid)
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...
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Cylinder (redirect from Elliptic cylinder)
hyperbola is called an elliptic cylinder, parabolic cylinder and hyperbolic cylinder, respectively. These are degenerate quadric surfaces. When the principal...
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Enriques–Kodaira classification (redirect from Classification of algebraic surface)
surfaces, all hyperelliptic surfaces, all Kodaira surfaces, some K3 surfaces, some abelian surfaces, and some rational surfaces are elliptic surfaces...
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In algebraic geometry, an elliptic singularity of a surface, introduced by Philip Wagreich in 1970, is a surface singularity such that the arithmetic genus...
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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...
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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...
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algebraic surfaces Ruled surface Cubic surface Veronese surface Del Pezzo surface Rational surface Enriques surface K3 surface Hodge index theorem Elliptic surface...
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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...
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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...
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Saddle point (redirect from Saddle surface)
hyperbolic paraboloid shape. Saddle surfaces have negative Gaussian curvature which distinguish them from convex/elliptical surfaces which have positive Gaussian...
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lateral conic surface, a quadric called conical quadric or quadratic cone. In a three-dimensional Cartesian coordinate system, an elliptic cone is the locus...
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Genus (mathematics) (redirect from Genus of topological surface)
applied to the Riemann surface of X {\displaystyle X} (its manifold of complex points). For example, the definition of elliptic curve from algebraic geometry...
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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...
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trivial square. Enriques surfaces are all projective (and therefore Kähler over the complex numbers) and are elliptic surfaces of genus 0. Over fields...
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David Mumford (section Classification of surfaces)
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...
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In mathematics, an abelian surface is a 2-dimensional abelian variety. One-dimensional complex tori are just elliptic curves and are all algebraic, but...
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ADE classification (redirect from Buckyball surface)
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...
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Amherst College. He studies, among other things, étale homotopy theory, elliptic surfaces, computer-based algebraic geometry (such as Gröbner basis), Torelli...
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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...
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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...
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Uniformization theorem (category Riemann surfaces)
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...
29 KB (3,387 words) - 14:54, 27 January 2025
In mathematics, Dolgachev surfaces are certain simply connected elliptic surfaces, introduced by Igor Dolgachev (1981). They can be used to give examples...
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Leaf spring (redirect from Quarter-elliptic leaf spring)
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...
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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...
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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 (...
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