Higher Castelnuovo theory
Journées de géométrie algébrique d'Orsay - Juillet 1992, Astérisque, no. 218 (1993), pp. 187-202. 
@incollection{AST_1993__218__187_0,
     author = {Eisenbud, David and Green, Mark and Harris, Joe},
     title = {Higher {Castelnuovo} theory},
     booktitle = {Journ\'ees de g\'eom\'etrie alg\'ebrique d'Orsay - Juillet 1992},
     series = {Ast\'erisque},
     pages = {187--202},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {218},
     year = {1993},
     language = {en},
     url = {http://archive.numdam.org/item/AST_1993__218__187_0/}
}
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Eisenbud, David; Green, Mark; Harris, Joe. Higher Castelnuovo theory, dans Journées de géométrie algébrique d'Orsay - Juillet 1992, Astérisque, no. 218 (1993), pp. 187-202. http://archive.numdam.org/item/AST_1993__218__187_0/

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[2] C. Ciliberto. Hilbert functions of finite sets of points and the genus of a curve in a projective space, Space Curves, Rocca di Papa, 1985, ed. F. Ghione, C. Peskine, and E. Sernesi, 1987.

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[10] J. G. Semple and L. Roth, Introduction to Algebraic Geometry, Clarendon Press, Oxford (1949).