Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-13T11:30:18.193Z Has data issue: false hasContentIssue false

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*
Affiliation:
Department of Mathematics, Acadia University, Woljville, NS BOP 1X0
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Type
Research Article
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), 2528.Google Scholar
2. Davis, E., Geramita, A.V. and Maroscia, P., Perfect homogeneous ideals: Dubreil's theorems revisited, Bull. Sc. Math. (2) 108(1984), 143185.Google Scholar
3. Davis, E., Geramita, A.V. and Orecchia, F., Gorenstein algebras and the Cayley-Bacherach theorem, PAMS 93(1985), 593597.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., 2279.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), 528555.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), 443452.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), 8596.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), 5783.Google Scholar