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The Conductor of Points Having the Hilbert Function of a Complete Intersection in P2

Published online by Cambridge University Press:  20 November 2018

Amar Sodhi
Amar Sodhi*
Affiliation:
Department of Mathematics, Acadia University, Woljville, NS BOP 1X0
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Abstract

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Let A be the coordinate ring of a set of s points in pn(k). After examining what the Hilbert function of A tells us about the conductor of A, we then determine the possible conductors for those coordinate rings which have the Hilbert function of a complete intersection in P2(k).

Keywords

14M1014A0513H15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 1 , 01 December 1991 , pp. 167 - 179
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Davis, E., Complete intersections of codimension 2 in P2; the Bezout-Jacobi-Segre theorem revisited, Rend. Sem. Mat. Torino 42(1984), 25–28.Google Scholar
2. Davis, E., Geramita, A.V. and Maroscia, P., Perfect homogeneous ideals: Dubreil's theorems revisited, Bull. Sc. Math. (2) 108(1984), 143–185.Google Scholar
3. Davis, E., Geramita, A.V. and Orecchia, F., Gorenstein algebras and the Cayley-Bacherach theorem, PAMS 93(1985), 593–597.Google Scholar
4. Greene, C.and Kleitman, D.J., Proof techniques in the theory of finite sets. M.Studies, A.A. in Combinatorics (Rota, G.C., éd.), Math. Assoc, of America, Washington, D.C., 22–79.Google Scholar
5. Geramita, A.V. and Maroscia, P., The ideal of forms vanishing at a finite set of points, J. of Alg. (2) 20(1984), 528–555.Google Scholar
6. Geramita, A.V., Maroscia, P. and L. Roberts, On the Hilbert function of a reduced K-algebra, J. Lond. Math. Soc. 28(1983), 443–452.Google Scholar
7. Geramita, A.V., On the Hilbert function of a reduced K-algebra. The Curves Seminar at Queen's Vol. II, Queen's Papers in Pure and Applied Mathematics 61, Kingston, Ontario, Canada.Google Scholar
8. Hartshorne, R., Algebraic geometry. Graduate texts in Mathematics, 52, Springer-Verlag, New York-Berlin, 1977.Google Scholar
9. Orecchia, F., Points in generic position and the conductor of curves with ordinary singularities, J. Lond. Math. Soc. 24(1981), 85–96.Google Scholar
10. Sodhi, A., A note on the intersection of a hypersurface with a finite set of points in P”. The Curves Seminar at Queen's Vol. VI, Queen's Papers in Pure and Applied Mathematics, 83, Kingston, Ontario, Canada.Google Scholar
11. Stanley, R., Hilbert functions of graded algebras, Adv. in Math. 28(1978), 57–83.Google Scholar