The Weierstrass subgroup of a curve has maximal rank. Martine Girard, David R. Kohel and Christophe Ritzenthaler ∗†‡ Abstract We show that the Weierstrass points of the generic curve of genus g over an algebraical

Source URL: iml.univ-mrs.fr

• Algebraic geometry
• Mathematical analysis
• Algebra
• Algebraic curves
• Elliptic curve
• Weierstrass point
• Hyperelliptic curve
• Moduli space
• Kummer surface
• StoneWeierstrass theorem

Arithmetic on Abelian and Kummer varieties Notes of a talk given for the Lfant Algorithmic Number Theory Seminar — Bordeaux. Based on earlier talks given in Grenoble and Caen. Abstract. In this talk we give an outline

Source URL: www.normalesup.org

• Operator theory
• Differential geometry
• Analytic number theory
• Elliptic curve
• Group theory
• Torsion tensor
• Divisor
• Differential forms on a Riemann surface
• Table of stars with Bayer designations

. Genus 2 formulae based on Theta functions and their implementation Pierrick Gaudry

Source URL: mathsci.ucd.ie

• Riemann surfaces
• Algebraic surfaces
• Analytic number theory
• Elliptic curve
• Group theory
• Kummer surface
• Pi
• Theta function

Point counting in genus 2: reaching 128 bits P. Gaudry ´ Schost

Source URL: www.hyperelliptic.org

• Differential geometry
• Curvature
• Curves
• Algebraic surfaces
• Group theory
• Abelian variety
• Resultant
• Elliptic curve
• Torsion tensor
• Kummer surface
• Polynomial
• Torsion of a curve

EXPLICIT KUMMER SURFACE FORMULAS FOR ARBITRARY CHARACTERISTIC ¨ JAN STEFFEN MULLER Abstract. If C is a curve of genus 2 defined over a field k and J is its Jacobian, then we can associate a hypersurface K in P3 to J,

Source URL: www.math.uni-hamburg.de

The Arithmetic of Hyperelliptic Curves E. V. Flynn∗ , Mathematical Institute, University of Oxford Abstract We summarise recent advances in techniques for solving Diophantine problems on hyperelliptic curves; in partic

Source URL: eprints.maths.ox.ac.uk

• Elliptic curve
• Kummer surface
• Algebraic number field
• Hyperelliptic curve
• Hyperelliptic curve cryptography
• Trace Zero Cryptography
• Abstract algebra
• Algebraic geometry
• Algebraic curves

Picard-Einstein Metrics and Class Fields Connected with Apollonius Cycle R-P. Holzapfel with Appendices by A. Pi~neiro, N. Vladov August 17, 1998

Source URL: edoc.hu-berlin.de

• Projective geometry
• Elliptic curve
• Quadric
• Enriques–Kodaira classification
• Curve
• Circle
• Algebraic curve
• Kummer surface
• Lie sphere geometry
• Geometry
• Algebraic geometry
• Algebraic surfaces

The Arithmetic of Hyperelliptic Curves E. V. Flynn∗ , Mathematical Institute, University of Oxford Abstract We summarise recent advances in techniques for solving Diophantine problems on hyperelliptic curves; in partic

Source URL: people.maths.ox.ac.uk

• Elliptic curve
• Kummer surface
• Algebraic number field
• Hyperelliptic curve
• Hyperelliptic curve cryptography
• Trace Zero Cryptography
• Abstract algebra
• Algebraic geometry
• Algebraic curves

The group law on the Jacobian of a curve of genus 2 E. V. Flynn, Mathematical Institute, University of Oxford Abstract An explicit description is given of the group law on the Jacobian of a curve C of genus 2. The Kummer

Source URL: people.maths.ox.ac.uk

• Algebraic surfaces
• Kummer surface

CANONICAL HEIGHTS ON THE JACOBIANS OF CURVES OF GENUS 2 AND THE INFINITE DESCENT E.V. FLYNN AND N.P. SMART Abstract. We give an algorithm to compute the canonical height on a Jacobian of a curve of genus 2. The computati

Source URL: people.maths.ox.ac.uk

• Algebraic number theory
• Analytic number theory
• Elliptic curve
• Group theory
• Kummer surface
• Algebraic number field
• P-adic number
• Prime number
• Abstract algebra
• Mathematics
• Field theory