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A criterion for intersection multiplicity one

Published online by Cambridge University Press:  22 January 2016

Rüdiger Achilles ,
Craig Huneke  and
Wolfgang Vogel
Rüdiger Achilles
Affiliation:
Martin-Luther-University, Department of Mathematics 4010 Halle German Democratic Republic
Craig Huneke
Affiliation:
Purdue University, Department of Mathematics West Lafayette, Indiana 47907, USA
Wolfgang Vogel
Affiliation:
Martin-Luther-University, Department of Mathematics 4010 Halle German Democratic Republic
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Let X and Y be any pure dimensional subschemes of Pnk over an algebraically closed field K and let I(X) and I(Y) be the largest homogeneous ideals in K[x0,…, xn] defining X and Y, respectively. By a pure dimensional subscheme X of Pnk we shall always mean a closed pure dimensional subscheme without imbedded components, i.e., all primes belonging to I(X) have the same dimension.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 100 , December 1985 , pp. 49 - 63
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1985

References

[ 0 ] Achilles, R., On the intersection multiplicity of improper components in algebraic geometry, Beitrage Algebra Geom., 19 (1985), 113–129.Google Scholar
[ 1 ] Avramov, L. L., Homology of local flat extensions and complete intersection defects, Math. Ann., 228 (1977), 27–37.CrossRefGoogle Scholar
[ 2 ] Budach, L. und Vogel, W., Cohen-Macaulay Moduln und der Bezoutsche Satz, Monatsh. Math., 73 (1969), 97–111.CrossRefGoogle Scholar
[ 3 ] Fulton, W., Intersection theory. Ergebnisse der Mathematik, 3. Folge. Springer-Verlag New York-Heidelberg-Berlin-Tokyo, 1984.Google Scholar
[ 4 ] Grobner, W., Moderne algebraische Geometrie, Springer-Verlag Wien und Innsbruck, 1949.CrossRefGoogle Scholar
[ 5 ] Grothendieck, A., Elements de geometrie algebrique, I.H.E.S., Publ. Math., Paris, No. 24 (1965).Google Scholar
[ 6 ] Herzog, J. und Kunz, E., Der kanonische Modul eines Cohen-Macaulay-Rings, Lecture Notes in Math., No. 238, Springer-Verlag Berlin-Heidelberg-New York, 1971.Google Scholar
[ 7 ] Kiehl, R. und Kunz, E., Vollstandige Durchschnitte und p-Basen, Arch. Math. (Basel), 16 (1965), 348–362.Google Scholar
[ 8 ] Lazarsfeld, R., Excess intersection of divisors, Compositio Math., 43 (1981), 281–296.Google Scholar
[ 9 ] Matsumura, H., Commutative algebra, Benjamin, New York, 1970.Google Scholar
[10] Nagata, M., Local rings, Interscience PubL, New York, 1962.Google Scholar
[11] Patil, D. P. and Vogel, W., Remarks on the algebraic approach to intersection theory, Monatsh. Math., 96 (1983), 233–250.CrossRefGoogle Scholar
[12] Samuel, P., Méthodes d’algébre abstraite en géeométrie algébrique, Ergebnisse der Mathematik, Neue Folge. Springer-Verlag Berlin-Göttingen-Heidelberg, 1955.Google Scholar
[13] Selder, E., Lokale analytische Schnittmultiplizitäten, Dissertation, Universitat Osnabrück, 1981.Google Scholar
[14] Serre, J.-P., Algèbre locale. Multiplicités. Lecture Notes in Math., No. 11, Springer-Verlag Berlin-Heidelberg-New York, 1965.Google Scholar
[15] Severi, F., Osservazioni sul Restsatz per le curve iperspaziali, Atti della R. Ace. delle Scienze di Torino, 1908.Google Scholar
[16] Severi, F. II, concetto generale di multiplicita della soluzioni per sistemi de equazioni algebriche e la teoria del’eliminazione, Annali di Math., 26 (1947), 221–270.CrossRefGoogle Scholar
[17] Stückrad, J. and Vogel, W., An algebraic approach to the intersection theory. In: The curves seminar at Queen’s Vol. II, 1–32. Queen’s papers in pure and applied mathematics, No. 61, Kingston, Ontario, Canada, 1982.Google Scholar
[18] Vogel, W., Lectures on results on Bezout’s Theorem, Lecture Notes, Tata Institute of Fundamental Research of Bombay (Notes by D. P. Patil), Springer-Verlag Berlin-Heidelberg-New York, Tokyo, 1984.Google Scholar
[19] Waerden, B. L. van der, Algebra, 5. Aufl. der Modernen Algebra, 2. gTeil. Springer-Verlag Berlin-Heidelberg-New York, 1967.Google Scholar
[20] Weil, A., Foundations of algebraic geometry, Amer. Math. Soc, Providence, R. I., 1962.Google Scholar
[21] Zariski, O. and Samuel, P., Commutative algebra, Vol. I and II. D. van Nostrand Company, Princeton, 1958 and 1960.CrossRefGoogle Scholar