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Real forms of cusp singularities

Published online by Cambridge University Press:  24 October 2008

C. T. C. Wall
Affiliation:
Department of Pure Mathematics, University of Liverpool, Liverpool L69 3BX

Extract

Cusp singularities were introduced and described in detail in Hirzebruch's fundamental paper [3] (se recall some of the basic results in § 1 below). They form a natural and well-behaved class, included in Laufer's ‘minimally elliptic’ singularities [5]. Those which occur on hypersurfaces appear also as hyperbolic singularities in Arnold's [1] classification of 1-modal singularities.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Arnold, V. I.. Critical points of smooth functions and their normal forms. Russ. Math. Surveys 30 v (1975), 175.CrossRefGoogle Scholar
[2]Ebeling, W. and Wall, C. T. C.. Kodaira singularities and an extension of Arnold's strange duality. Compositio Math., 56 (1985), 377.Google Scholar
[3]Hirzebruch, F. E. P.. Hilbert modular surfaces. L' Enseignement Math. 19 (1973), 183281.Google Scholar
[4]Inoue, M.. New surfaces with no meromorphic functions II. In Complex Analysis and Algebraic Geometry, ed. Baily, W. C. and Shioda, T. (Cambridge University Press and Iwanami Shoten, 1977), 91106.CrossRefGoogle Scholar
[5]Laufer, H.. On minimally elliptic singularities. Amer. J. Math. 99 (1977), 12571295.CrossRefGoogle Scholar
[6]Meeks, W. H. and Scott, G. P.. Finite group actions on 3-manifolds, to appear.Google Scholar
[7]Nakamura, I.. Inoue-Hirzebruch surfaces and a duality of hyperbolic unimodular singularities. Math. Ann. 252 (1980), 221235.CrossRefGoogle Scholar
[8]Neumann, W. D.. Geometry of quasihomogeneous surface singularities. In Singularities, ed. Orlik, P., Proc. Symp. in Pure Math., vol 40, part 2 (Amer. Math. Soc., 1983), 245258.CrossRefGoogle Scholar
[9]Pinkham, H. C.. Automorphisms of cusps and Inoue-Hirzebruch surfaces. Compositio Math. 52 (1984), 299313.Google Scholar
[10]Scott, G. P.. The geometries of 3-manifolds. Bull. London Math. Soc. 15 (1983), 401487.CrossRefGoogle Scholar
[11]Wahl, J. M.. Derivations, automorphisms and deformations of quasi-homogeneous singularities. In Singularities, ed. Orlik, P., Proc. Symp. in Pure Math., vol. 40, part 2 (Amer. Math. Soc., 1983), 613624.CrossRefGoogle Scholar
[12]Waldhausen, F.. On irreducible 3-manifolds which are sufficiently large. Ann. of Math. 87 (1968), 5688.CrossRefGoogle Scholar
[13]Wall, C. T. C.. A second note on symmetry of singularities. Bull. London Math. Soc. 12 (1980), 347354.CrossRefGoogle Scholar
[14]WALL, C. T.. Topological invariance of the Milnor number mod 2. Topology 22 (1983), 345350.CrossRefGoogle Scholar