In mathematics, a hyperelliptic surface, or bi-elliptic surface, is a surface whose Albanese morphism is an elliptic fibration. Any such surface can be written as the quotient of a product of two elliptic curves by a finite abelian group.
Hyperelliptic surfaces form one of the classes of surfaces of Kodaira dimension 0 in the Enriques–Kodaira classification.
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mathematics, a hyperellipticsurface, or bi-elliptic surface, is a surface whose Albanese morphism is an elliptic fibration. Any such surface can be written...
elliptic function. Likewise, genus g surfaces have Riemann surface structures, as (compactifications of) hyperellipticsurfaces y2 = Q(x), where Q is a complex...
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...
Enriques surfaces, a variation on the notion of Enriques surfaces that only exist in characteristic two Hyperellipticsurfaces or bielliptic surfaces; quasi-hyperelliptic...
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...
Hyperelliptic curve cryptography is similar to elliptic curve cryptography (ECC) insofar as the Jacobian of a hyperelliptic curve is an abelian group...
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}\...
surfaces. b) Kodaira dimension 0. These are the K3 surfaces, abelian surfaces, hyperelliptic and quasi-hyperellipticsurfaces, and Enriques surfaces....
The Tobler hyperelliptical projection is a family of equal-area pseudocylindrical projections that may be used for world maps. Waldo R. Tobler introduced...
solvmanifolds; these are complex torus, hyperellipticsurface, Kodaira surface and Inoue surfaces S0, S+ and S−. The Inoue surfaces are constructed explicitly as...
non-orientable closed surface obtained in this way has an orientable double cover of genus two, and is therefore hyperelliptic. The proof then exploits...
double cover of an elliptic curve. 2. A bielliptic surface is the same as a hyperellipticsurface. bifid 1. Split into two equal parts 2. A bifid map...
equal-area polyhedral projection, used for geodesic grids. Tobler hyperelliptical Werner If the length of the line segment connecting two projected points...
1017/S0143385704001014. Katz, Mikhail G.; Sabourau, Stéphane (2006). "Hyperellipticsurfaces are Loewner". Proceedings of the American Mathematical Society....
the hyperelliptic quotient of the Riemann surface proves the filling area conjecture in this case. Other systolic ramifications of hyperellipticity have...
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...
example, hyperelliptic curves have a g 2 1 {\displaystyle g_{2}^{1}} since | K C | {\displaystyle |K_{C}|} defines one. In fact, hyperelliptic curves have...
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