By Laurent Gruson, Christian Peskine (auth.), Patrick Le Barz, Yves Hervier (eds.)

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2n! , 1,X C en Ie plan d'intersection requises car ni,x P. 1 H 1i *j) est a les proprietes n' . d. d. est Z et correspond au , 24 P, point (i. e. /!!! 2 que les classes des coefficients du reste de la division euclidienne de par ce sous espace vectoriel est aussi cngendre par les ~x; classes des coefficients des restes des divisions n. euclidiennes de T par les polymomes (Z-zi) 1,X ni,x T * O. pour utilisons alors Ie systeme regulier de parametres (a,b,c,d) defini au debut de ce paragraphe, ct remarquons que compte tenu de la construction de classes de S(O) et a sont les memes a S, les un coefficient invcr- sible pres.

O Dualisant a par rapport OS' nous obstenons une suite exacte o v Qs/p 3 ~ ~ Mais la derniere application de cette suite contenue dans (ou Js(a,s) car Ie morphisme S ~ p3 Js a son image est l'ideal de T dans n'est plat en aucun point de S) T Remarquons de plus que l'application a son conoyau de codimension au moins 2 a Considerons maintenant sa restriction de a g, correspondant courbe de degre s un plan general restriction de H n C l'ideal de la section plane Ie fibre projectif Q F S sur p3 dans F.

H 10 K' H ~ HA and Hw H, so the (birational) blows up the other sets For example, 11K HK,H A , , · · · are in n: T Only has codimension plane cuspidal cubics in ~3), 2 (there and for a given = n- 1 (C) {(c,r,c*); r = a (uniquely determined) cuspidall cubic union a line through the flex Since "a line through the flex" corresponds to "a plane containing the cusp tangent of C", we see that dim n- 1 (e) = 1. The set namely 8; 11~ specialize to these. 7: has the largest codimension, (=H 6 ,) all degenerations without an embedded point In this case, n- 1 (e) has dimension the tangent curve is determined by choosing 4 point- planes through the line e d ' which satisfy one relation re between the cross-ratios (of the points and planes) (see e.