mathematics, a hyperelliptic surface, or bi-elliptic surface, is a surface whose Albanese morphism is an elliptic fibration. Any such surface can be written...

also gets singular and supersingular Enriques surfaces in characteristic 2, and quasi-hyperelliptic surfaces in characteristics 2 and 3. The Enriques–Kodaira...

In algebraic geometry, a hyperelliptic curve is an algebraic curve of genus g > 1, given by an equation of the form y 2 + h ( x ) y = f ( x ) {\displaystyle...

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

cubic surfaces, Veronese surface, del Pezzo surfaces, ruled surfaces κ = 0 : K3 surfaces, abelian surfaces, Enriques surfaces, hyperelliptic surfaces κ = 1:...

Enriques surfaces, a variation on the notion of Enriques surfaces that only exist in characteristic two Hyperelliptic surfaces or bielliptic surfaces; quasi-hyperelliptic...

converse is not true. The simplest examples where this happens are hyperelliptic surfaces, finite quotients of a complex torus of complex dimension 2, which...

number of 16 double points. Any such surface is the Kummer variety of the Jacobian variety of a smooth hyperelliptic curve of genus 2; i.e. a quotient of...

curve for higher genus hyperelliptic curves arises in the same way with higher power monomials in x. Otherwise, for non-hyperelliptic C which means g is at...

Shafarevich in a seminar introduced an important numerical invariant of surfaces with the notation κ. Shigeru Iitaka extended it and defined the Kodaira...

to all curves over the complex numbers. They include for example the hyperelliptic integrals of type ∫ x k d x Q ( x ) {\displaystyle \int {\frac {x^{k}\...

Hyperelliptic curve cryptography is similar to elliptic curve cryptography (ECC) insofar as the Jacobian of a hyperelliptic curve is an abelian group...

surfaces. b) Kodaira dimension 0. These are the K3 surfaces, abelian surfaces, hyperelliptic and quasi-hyperelliptic surfaces, and Enriques surfaces....

solvmanifolds; these are complex torus, hyperelliptic surface, Kodaira surface and Inoue surfaces S0, S+ and S−. The Inoue surfaces are constructed explicitly as...

(algebraic) Elkies trinomial curves Hyperelliptic curve Klein quartic Classical modular curve Erdős lemniscate Hurwitz surface Mandelbrot curve Polynomial lemniscate...

The Tobler hyperelliptical projection is a family of equal-area pseudocylindrical projections that may be used for world maps. Waldo R. Tobler introduced...

non-orientable closed surface obtained in this way has an orientable double cover of genus two, and is therefore hyperelliptic. The proof then exploits...

elliptic functions Elliptic integral Complex multiplication Weil pairing Hyperelliptic curve Klein quartic Modular curve Modular equation Modular function...

\lambda _{1},\lambda _{2},L)} where Σ {\displaystyle \Sigma } is a hyperelliptic curve called the spectral curve, λ {\displaystyle \lambda } is a meromorphic...

equal-area polyhedral projection, used for geodesic grids. Tobler hyperelliptical Werner If the length of the line segment connecting two projected points...

Griffiths in 1980 with thesis Semistable Degenerations of Enriques' and Hyperelliptic Surfaces. From 1980 he was an instructor and from 1982 an assistant professor...

canonical divisor, or if C is a hyperelliptic curve and D linearly equivalent to an integral multiple of a hyperelliptic divisor. The Clifford index of...

Bordin of the Académie des Sciences of Paris for their work on hyperelliptic surfaces. De Franchis and Bagnera were Invited Speakers at the ICM in 1908...

1017/S0143385704001014. Katz, Mikhail G.; Sabourau, Stéphane (2006). "Hyperelliptic surfaces are Loewner". Proceedings of the American Mathematical Society....

Fermat curve Sinusoidal spiral Superellipse Hurwitz surface Elkies trinomial curves Hyperelliptic curve Classical modular curve Cassini oval Bowditch...

the hyperelliptic quotient of the Riemann surface proves the filling area conjecture in this case. Other systolic ramifications of hyperellipticity have...

double cover of an elliptic curve. 2.  A bielliptic surface is the same as a hyperelliptic surface. bifid 1.  Split into two equal parts 2.  A bifid map...

linear systems is used in the classification of algebraic curves. A hyperelliptic curve is a curve C {\displaystyle C} with a degre 2 {\displaystyle 2}...

Fuller projection, is a kind of polyhedral map projection of the Earth's surface onto the unfolded net of an icosahedron. The resulting map is heavily interrupted...

surface maximizes the length of the systole (Schmutz 1993). As a hyperelliptic Riemann surface, it arises as the ramified double cover of the Riemann sphere...