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Some enumerative formulae for algebraic curves

Published online by Cambridge University Press:  24 October 2008

I. G. Macdonald
I. G. Macdonald
Affiliation:
University of Manchester
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Extract

This paper is in two parts. In Part I we are concerned with one or more linear series on an algebraic curve; we consider a set of points on the curve which are contained with assigned multiplicities in a set of each of the linear series and, by persistent use of Severi's equivalence relation for the united points of an algebraic correspondence with valency, we derive formulae for the number of such sets of points when the constants involved are such as to make this number finite. All this is essentially a generalization of the formula for the number of points in the Jacobian set of a linear series of freedom 1, and the main result is Theorem 3.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 54 , Issue 4 , October 1958 , pp. 399 - 416
Copyright
Copyright © Cambridge Philosophical Society 1958

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References

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