By Laurent Gruson, Christian Peskine (auth.), Patrick Le Barz, Yves Hervier (eds.)
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289 (10 decembre 1979). E. Schwarzenberger. The secant bundle of a projective variety. Proc. of the London Math. Soc. Vol XIV, 1964. [5] L. Szpiro. Travaux de Kempf, Kleiman, Laksov sur les diviseurs exceptionnels. Semina ire Bourbaki. Juin 1972, expo no 417. [6] L. Szpiro. Equations defining space curves. Tata Institute. R. O. Box 1053, Blindern, OSLO 3 NORVEGE SECTION PLANE D'UNE COURBE GAUCHE: POSTULATION par Laurent GRUSON et Christian PESKINE Dans cette note, on voit qu'une simple transcription de la demonstration, fournie par Barth ([1]), du theoreme de stabilite de Grauert-Mulich demontre Ie resultat suivant: Lemme (Laudal): Soit C une courbe integre de degre p 3 (1}, non contenue dans une surface de degre Si la section plane genera Ie de une courbe plane de degre Soient p F M, nous noterons C p3 V p3 V p3.
K-vector space, by = YUZ, with dim (YnZ) = 0, we will Also, y·z is defined to be equal to the length 54 6 ytlz ' of and i f (Y'Z)x is, by definition, the length of X€X, GyIIZ,x. If is a subscheme of y 21 is X, coherent on X, jfl y stands for ;/sGy. If s is a section Of:t, at any point of divisors. s:= 0 means that the stalk of s is 0 is also used to denote linear equivalence of X; _ Without explicit mention we shall assume all the schemes under consideration to be complete. R. R. is an abbreviation for the Grothendieck-Serre-Riemann-Roch duality theorem (see [7], [11]) which, in the case of curves, readR out as follows: '" vl,J.
Box 1053, Blindern, OSLO 3 NORVEGE SECTION PLANE D'UNE COURBE GAUCHE: POSTULATION par Laurent GRUSON et Christian PESKINE Dans cette note, on voit qu'une simple transcription de la demonstration, fournie par Barth ([1]), du theoreme de stabilite de Grauert-Mulich demontre Ie resultat suivant: Lemme (Laudal): Soit C une courbe integre de degre p 3 (1}, non contenue dans une surface de degre Si la section plane genera Ie de une courbe plane de degre Soient p F M, nous noterons C p3 V p3 V p3. of-module (m}) 00 p*(M(n}}.