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A group law on smooth real quartics having at least 3 real branches

Johan Huisman (2002)

Journal de théorie des nombres de Bordeaux

Let C be a smooth real quartic curve in ℙ 2 . Suppose that C has at least 3 real branches B 1 , B 2 , B 3 . Let B = B 1 × B 2 × B 3 and let O ∈ B . Let τ O be the map from B into the neutral component Jac ( C ) ( ℝ ) 0 of the set of real points of the jacobian of C , defined by letting τ O ( P ) be the divisor class of the divisor ∑ P i - O i . Then, τ O is a bijection. We show that this allows an explicit geometric description of the group law on Jac ( C ) ( ℝ ) 0 . It generalizes the classical geometric description of the group law on the neutral component of the set of real points of...

Cubic differential forms and the group law on the Jacobian of a real algebraic curve

J. Huisman (2003)

Bollettino dell'Unione Matematica Italiana

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...

Décomposition du Galois-module des entiers d'une extension cyclique de degré premier d'un corps de nombres ou d'un corps local

Françoise Bertrandias (1979)

Annales de l'institut Fourier

Soit A un anneau de Dedekind, de corps des fractions K , et soit L une extension galoisienne de K , dont le groupe de Galois G est cyclique d’ordre premier. On note B la clôture intégrale de A dans L . Il existe une unique décomposition du A [ G ] -module B en somme directe de sous-modules indécomposables. On détermine cette décomposition lorsque K est un corps local ou un corps de nombres. Le résultat dépend d’une part des caractères irréductibles de G sur K , d’autre part des nombres de ramification associés...

On ramification locus of a polynomial mapping

Zbigniew Jelonek (2003)

Banach Center Publications

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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