By E. Arrondo, M. Pedreira, I. Sols (auth.), Edoardo Ballico, Ciro Ciliberto (eds.)

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Extra info for Algebraic Curves and Projective Geometry: Proceedings of the Conference held in Trento, Italy, March 21–25, 1988

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C ne sont de v6rifier: C o m m e X(C) = d(k+s-2)-g(C)+l. est ~quivalent = F, Ceci ~: on dit, g(C) > G(d,s)-(s3+3s2+4s)/6. (b) Soit Y la c o u r b e On a deg(Y) de C, p a r = s2-s-l. 3 et p a r m a p p i n g ~ y ~ H -~O. mH(s-2) : H l ( ~ y ( S - 2 ) ) il v i e n t Comme n-(2) S est -~ < s+2. int~gre, (s,s-l) . C e t t e s-2. Si g(C) Y, (s,s-l). D6m: lie l'hypoth~se intersection s2-s-2. En g(C) C l'est comme utilisant deux. On par g(C) en des et obtient liaison la supposer aussi On = O alors D'apr~s h°(~y(S-l)) intersection droite.

N. c u r v e cutting Z on ~ is a question on the smoothability of C(Zg: we want a smoothing of CC2D by a flat family which fixes the p o i n t s o f Z. n. c u r v e s C w a s s t u d i e d by Peskine 34 and Szpiro Cwho proved i n [PSI t h a t C i s s m o o t h a b l e when all numbers s i-rj are positiveD and by Sauer C[S]D who solved problem sequence showing that C is smoothable if and only i f, to the C29 above, s n > _ r n _ 2 f o r all n. n. c u r v e , h o w e v e r any set Z to a set of points in generic over 7 can such smoothing position.

U-l. REFERENCES [GAC] [CGO] [E] [GM] [GP] [HI [AG] [0] [PS] IS] Arbarello A. , C o r n a l b a M. A. , H a r r i s J. GEOMETRY O F A L G E B R A I C CURVES Springer igS~. Ciliberto C. , G e r a m i t a A. , O r e c c h i a F. Some remarks on a theorem of Hilbert-Burch ( t o a p p e a r i n B o l l . UMI 1 9 8 8 9 . Ellingsrud G. Sur le sch@ma de Hilbert des variet@s alg@briques de ~e a c6ne de Cohen-Macaulay. Ann. Sci. Ec. N o r m . Sup. 4 C 8 9 C I g V B D 4 2 3 - 4 3 2 . Geramita A. , M i g l i o r e J.

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