Gorenstein algebras and the Cayley-Bacharach theorem
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- by E. D. Davis, A. V. Geramita and F. Orecchia PDF
- Proc. Amer. Math. Soc. 93 (1985), 593-597 Request permission
Abstract:
This paper is an examination of the connection between the classical Cayley-Bacharach theorem for complete intersections in ${{\mathbf {P}}^2}$ and properties of graded Gorenstein algebras.References
- Yôichi Aoyama and Shirô Gotô, On the type of graded Cohen-Macaulay rings, J. Math. Kyoto Univ. 15 (1975), 19–23. MR 364229, DOI 10.1215/kjm/1250523116 E. Davis and P. Maroscia, Complete intersections in ${{\mathbf {P}}^2}$, Proc. Conf. on Complete Intersections (Acireale, June 1983), Lecture Notes in Math., (in press). W. Gröbner, Über Irreduzibel Ideale in Kommutativen Ringen, Math. Ann. 110 (1934), 197-222.
- Jürgen Herzog and Ernst Kunz (eds.), Der kanonische Modul eines Cohen-Macaulay-Rings, Lecture Notes in Mathematics, Vol. 238, Springer-Verlag, Berlin-New York, 1971. Seminar über die lokale Kohomologietheorie von Grothendieck, Universität Regensburg, Wintersemester 1970/1971. MR 0412177
- Irving Kaplansky, Commutative rings, Allyn and Bacon, Inc., Boston, Mass., 1970. MR 0254021
- Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0155856
- Ferruccio Orecchia, Points in generic position and conductors of curves with ordinary singularities, J. London Math. Soc. (2) 24 (1981), no. 1, 85–96. MR 623673, DOI 10.1112/jlms/s2-24.1.85
- C. Peskine and L. Szpiro, Liaison des variétés algébriques. I, Invent. Math. 26 (1974), 271–302 (French). MR 364271, DOI 10.1007/BF01425554
- J. G. Semple and L. Roth, Introduction to Algebraic Geometry, Oxford, at the Clarendon Press, 1949. MR 0034048
- Richard P. Stanley, Hilbert functions of graded algebras, Advances in Math. 28 (1978), no. 1, 57–83. MR 485835, DOI 10.1016/0001-8708(78)90045-2
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 593-597
- MSC: Primary 14M05; Secondary 13H10, 14M10
- DOI: https://doi.org/10.1090/S0002-9939-1985-0776185-6
- MathSciNet review: 776185