Type of surface singularity used in algebraic geometry
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In algebraic geometry, an elliptic singularity of a surface, introduced by Wagreich (1970), is a surface singularity such that the arithmetic genus of its local ring is 1.
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In algebraic geometry, an ellipticsingularity of a surface, introduced by Wagreich (1970), is a surface singularity such that the arithmetic genus of...
general enough to include all non-singular cubic curves; see § Elliptic curves over a general field below.) An elliptic curve is an abelian variety – that...
that is), elliptic curves over number fields. The product of any elliptic curve with any curve is an elliptic surface (with no singular fibers). All...
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see...
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...
supersingular elliptic curves form a certain class of elliptic curves over a field of characteristic p > 0 with unusually large endomorphism rings. Elliptic curves...
the theory of elliptic curves E that have an endomorphism ring larger than the integers. Put another way, it contains the theory of elliptic functions with...
In mathematics, the Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This...
Tate, John (1975), "Algorithm for determining the type of a singular fiber in an elliptic pencil", in Birch, B.J.; Kuyk, W. (eds.), Modular Functions...
functions is to use elliptic curves: every lattice Λ determines an elliptic curve C/Λ over C; two lattices determine isomorphic elliptic curves if and only...
when integrated along paths, give rise to integrals that generalise the elliptic integrals to all curves over the complex numbers. They include for example...
two-dimensional singularities, Annals of Mathematics Studies, 71, Princeton University Press Laufer, Henry B. (1977), "On minimally ellipticsingularities", American...
is called an elliptic curve. While this model is the simplest way to describe hyperelliptic curves, such an equation will have a singular point at infinity...
the unit disc. This function is explicitly constructed in the theory of elliptic functions. If f {\textstyle f} omits two values, then the composition of...
In mathematics, elliptic units are certain units of abelian extensions of imaginary quadratic fields constructed using singular values of modular functions...
back to the studies of Pierre de Fermat on what are now recognized as elliptic curves; and has become a very substantial area of arithmetic geometry both...
equations of the branches. For describing a singularity, it is worth to translate the curve for having the singularity at the origin. This consists of a change...
a continuous family of images of elliptic curves. (These curves are singular in X, unless X happens to be an elliptic K3 surface.) A stronger question...
harmonic function with the same singularity, so in this case the harmonic function is not determined by its singularities; however, we can make the solution...
then P {\displaystyle P} is said to be analytically hypoelliptic. Every elliptic operator with C ∞ {\displaystyle C^{\infty }} coefficients is hypoelliptic...
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