$C_{ab}$ 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, HumboldtUniversität zu Berlin (ISSN 08630976), 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, HumboldtUniversität zu Berlin (ISSN 08630976), 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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