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Prime ideals and postulation formulae

Published online by Cambridge University Press:  24 October 2008

L. S. Goddard
L. S. Goddard
Affiliation:
The United CollegeThe UniversitySt Andrews
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Extract

1. In this paper we find explicitly the base for the prime ideal associated with any irreducible Vd−1 on a Segre variety, or a Veronesean variety, Vd. This work extends that of an earlier paper (1) in which the base was found when the Vd−1 is a complete intersection of Vd with one primal. As particular examples we can write down the base for any irreducible curve on a quadric surface, a Veronese surface or a Del Pezzo surface. We also show how the base for any prime ideal changes under a Veronesean transformation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 44 , Issue 1 , January 1948 , pp. 43 - 49
Copyright
Copyright © Cambridge Philosophical Society 1948

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References

REFERENCES

(1)Goddard, . Proc. Cambridge Phil. Soc. 39 (1943), 35.CrossRefGoogle Scholar
(2)Severi, . R.C. Circ. mat. Palermo, 28 (1909), 33.CrossRefGoogle Scholar
(3)Room, . The Geometry of Determinantal Loci (Cambridge, 1938), p. 471.Google Scholar