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Let be a smooth real quartic curve in . Suppose that has at least real branches . Let and let . Let be the map from into the neutral component Jac of the set of real points of the jacobian of , defined by letting be the divisor class of the divisor . Then, is a bijection. We show that this allows an explicit geometric description of the group law on Jac. It generalizes the classical geometric description of the group law on the neutral component of the set of real points of...
In an earlier paper [6], we gave an explicit geometric description of the group law on the neutral component of the set of real points of the Jacobian of a smooth quartic curve. Here, we generalize this description to curves of higher genus. We get a description of the group law on the neutral component of the set of real points of the Jacobian of a smooth curve in terms of cubic differential forms. When applied to canonical curves, one gets an explicit geometric description of this group law by...
Soit un anneau de Dedekind, de corps des fractions , et soit une extension galoisienne de , dont le groupe de Galois est cyclique d’ordre premier. On note la clôture intégrale de dans . Il existe une unique décomposition du -module en somme directe de sous-modules indécomposables. On détermine cette décomposition lorsque est un corps local ou un corps de nombres. Le résultat dépend d’une part des caractères irréductibles de sur , d’autre part des nombres de ramification associés...
Let X be a smooth algebraic hypersurface in ℂⁿ. There is a proper polynomial mapping F: ℂⁿ → ℂⁿ, such that the set of ramification values of F contains the hypersurface X.
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