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Plücker formulae for singular space curves

Published online by Cambridge University Press:  27 April 2011

C. T. C. WALL
C. T. C. WALL*
Affiliation:
Department of Mathematical Sciences, The University of Liverpool, Mathematical Sciences Building, Liverpool L69 7ZL, U.K. e-mail: [email protected]
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Abstract

In [4] I extended the Plücker formulae to curves in Pn for any n, under fairly strong genericity hypotheses. In this paper we seek to weaken these hypotheses using the theory of excess intersections. The method applies to just one of the formulae (so the results are complete only for n=3), and for this we obtain a number which is a sum of local contributions, given by an explicit rule. We evaluate these contributions in the cases when they are determined by the terms of least order in the respective Taylor expansions, thus obtaining explicit formulae in numerous cases.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 151 , Issue 1 , July 2011 , pp. 129 - 143
Copyright
Copyright © Cambridge Philosophical Society 2011

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References

REFERENCES

[1]Fulton, W.Intersection theory, xii, 470 pp. (Springer-Verlag, 1984).CrossRefGoogle Scholar
[2]Griffiths, P. and Harris, J.Principles of algebraic geometry, xiv, 813 pp. (Wiley, 1978).Google Scholar
[3]Wall, C. T. C.Singular points of plane curves (London Math. Soc. student text 63), xii, 370 pp. (Cambridge University Press, 2004).CrossRefGoogle Scholar
[4]Wall, C. T. C.Plücker formulae for curves in high dimensions, Rend. Lincei Mat. Appl. 20 (2009), 159–177.Google Scholar
[5]Zeuthen, H. G.Sur les singularités ordinaires d'une courbe gauche et d'une surface développable, Ann. di Mat., ser 2, 3 (1869), 175–217. See also Comptes Rendus 67 (1868), p. 225.Google Scholar