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intersection theory — 1 results found.

      
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Bezout-type Theorems for the Affine Plane
C. R. Math. Rep. Acad. Sci. Canada Vol. 34 (4) 2012, pp. 112–126
Pinaki Mondal (Received: 2011/12/19)

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This article is mainly an announcement of some of the results from the article General Bezout-type theorems. We set up a framework for Bezout-type theorems for general affine varieties and apply it to study the “Bezout problem” on the affine plane. In particular, for a class of compactifications of the affine plane we compute the intersection numbers of the curves at infinity in terms of valuations at infinity, and generalize the Bernstein–Kushnirenko non-degeneracy criterion to the case of weighted degrees in possibly different systems of coordinates.

Cet article est principalement une annonce de quelques-uns des résultats de l’article General Bezout-type theorems. Nous construisons un système pour les théorèmes de type Bezout pour les variétés affines générales, et nous l’appliquons pour étudier le “Bezout problème” sur le plan affine. En particulier, pour une classe de compactifications du plan affine, nous calculons le nombre d’intersections des, courbes à l’infini en termes de valorisations à l’infini, et nous généralisons le critère de non-dégénérescence de Bernstein–Kushnirenko au cas de degrés pondérés dans les systèmes peut-être différents de coordonnées.

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