hyperelliptic

hyperelliptic
Describing an extension of elliptic functions to complex numbers

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  • hyperelliptic — hyperelliptic, geometric, al Math.: see hyper 3 …   Useful english dictionary

  • Hyperelliptic curve cryptography — is similar to elliptic curve cryptography (ECC) insomuch as the algebraic geometry construct of a hyperelliptic curve with an appropriate group law provides an Abelian group on which to do arithmetic. The use of hyperelliptic curves in… …   Wikipedia

  • Hyperelliptic curve — In algebraic geometry, a hyperelliptic curve (over the complex numbers) is an algebraic curve given by an equation of the form:y^2 = f(x)where f(x) is a polynomial of degree n > 4 with n distinct roots. A hyperelliptic function is a function from …   Wikipedia

  • Canonical bundle — In mathematics, the canonical bundle of a non singular algebraic variety V of dimension n is the line bundle which is the nth exterior power of the cotangent bundle Ω on V. Over the complex numbers, it is the determinant bundle of holomorphic n… …   Wikipedia

  • Enriques–Kodaira classification — In mathematics, the Enriques–Kodaira classification is a classification of compact complex surfaces into ten classes. For each of these classes, the surfaces in the class can be parametrized by a moduli space. For most of the classes the moduli… …   Wikipedia

  • Enriques-Kodaira classification — In mathematics, the Enriques Kodaira classification is a classification of compact complex surfaces. For complex projective surfaces it was done by Federigo Enriques, and Kunihiko Kodaira later extended it to non algebraic compact surfaces. It… …   Wikipedia

  • Doubling-oriented Doche–Icart–Kohel curve — A Doubling oriented Doche Icart Kohel curve of equation y2 = x3 − x2 − 16x In mathematics, the doubling oriented Doche–Icart–Kohel curve is a form in which an elliptic curve can be written. It is a special case of Weierstrass form and it is also… …   Wikipedia

  • Algebraic curve — In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with… …   Wikipedia

  • Systolic geometry — In mathematics, systolic geometry is the study of systolic invariants of manifolds and polyhedra, as initially conceived by Charles Loewner, and developed by Mikhail Gromov and others, in its arithmetic, ergodic, and topological manifestations.… …   Wikipedia

  • Trace Zero Cryptography — In the year 1998 Gerhard Frey firstly purposed using trace zero varieties for cryptographic purpose. These varieties are subgroups of the divisor class group on a low genus hyperelliptic curve defined over a finite field. These groups can be used …   Wikipedia

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