$C_{ab}$ Curves Jacobian Varieties Addition Law $C_{ab}$ Curves Jacobian Varieties Addition Law Reduction Algorithm Projective Model. A Geometric Interpretation of Reduction in the Jacobians of $C_{ab}$ Curves. Regis Blache Blache Regis Jorge Estrada Sarlabous Estrada Sarlabous Jorge Maria Petkova Petkova Maria Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 14 p.

A Geometric Interpretation of Reduction in the Jacobians of $C_{ab}$ Curves.

Regis Blache , Jorge Estrada Sarlabous , Maria Petkova

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 14 p.

MSC 2000

14H45 Special curves and curves of low genus
14H40 Jacobians, Prym varieties
14Q05 Curves
11G10 Abelian varieties of dimension $\gtr 1$
11G20 Curves over finite and local fields
11T71 Algebraic coding theory; cryptography

Abstract
In this paper, we show that the reduction of divisors in the Jacobian of a curve $C$ can be performed by considering the intersections of a suitable projective model of $C$ with quadrics in projective space. We apply this idea to certain projective model of elliptic and hyperelliptic curves on one hand, and to the canonical model of $C_{ab}$ curves on the other hand, and we generalize (and recover) some well known algorithms.

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