Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-05T02:00:43.416Z Has data issue: false hasContentIssue false

Recognizing singularities of surfaces in ℂP3

Published online by Cambridge University Press:  24 October 2008

M. G. Soares
Affiliation:
University of Liverpool.
P. J. Giblin
Affiliation:
University of Liverpool.

Extract

In this paper we consider complex projective surfaces V, defined by an equation of the form fn–1 (x, y, z) w + fn (x, y, z) = 0, where fi is homogeneous of degree i, and relate the geometry of the intersections of the piane projective curves fn–1 = 0 and fn = 0 with the singularities of V. The results we obtain clarify and generalize some of those presented by Bruce and Wall (3).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Arnol'd, V. I.Normal Forms of Functions in Neighbourhoods of Degenerate Criticai Points. Russ. Math. Surveys, 29:2, (1974), 1149.CrossRefGoogle Scholar
(2)Arnol'd, V. I.Local Normal Forma of Functions. Invetitiones Math. 35 (1976), 87109.CrossRefGoogle Scholar
(3)Bruce, J. W. and Wall, C. T. C.On the Classification of Cubie Surfaces. J. London Math. Soc. (2), 19 (1979), 245256.CrossRefGoogle Scholar
(4)Griffiths, Ph. and Harris, J.Principles of Algebraic Geometry, Wiley, New York (1978).Google Scholar
(5)Hartshorne, R.Algebraic Geometry. Graduate Texts in Mathematica 52, Springer (1977).Google Scholar
(6)Lamotke, K.The Topology of Complex Projective Varieties after S. Lefachetz. Topology, 20 (1981), 1551.CrossRefGoogle Scholar
(7)Milnor, J. W.Singular points of complex hypersurfaces. Ann. of Math. Studies No. 61, Princeton University Press (1968).Google Scholar
(8)Oka, M.On the cohomology structure of projective varieties, in Manifolds – Tokyo 1973, ed. Hattori, A., University of Tokyo Press (1974), pp. 137144.Google Scholar
(9)Siersma, D. Periodicities in Arnol'd's Lista of Singularities, Nordic Summer School/NAVF. Symp. in Maths. Oslo (1976).Google Scholar
(10)Spanier, E.Algebraic Topology. McGraw-Hill (1966).Google Scholar