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On deformation of curves and a formula of deligne

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Algebraic Geometry

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 961))

Abstract

We study deformations of germs of reduced complex curve singularities and of singular projective curves in some Pn(ℂ). In both cases a deformation is topologically trivial iff the Milnor numbers of the singularities are constant during the deformation. The Milnor number also occurs naturally in the degree of the singular Todd class of Baum-Fulton-MacPherson and in a formula of Deligne concerning the dimension of the base space of the semiuniversal deformation. Some applications of this fact are given in particular to the non-smooth-ability of certain curves.

This is a modified version of [G2]. The author gratefully acknowledges the financial support of the Deutsche Forschungsgemeinschaft and of the Stiftung Volkswagenwerk for a visit to the IHES, during which this paper was written.

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Authors and Affiliations

  1. Math. Institut der Universität, Wegeler Str. 10, D - 53, Bonn.

    Gert-Martin Greuel

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  1. Gert-Martin Greuel
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José Manuel Aroca Ragnar Buchweitz Marc Giusti Michel Merle

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© 1982 Springer-Verlag

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Greuel, GM. (1982). On deformation of curves and a formula of deligne. In: Aroca, J.M., Buchweitz, R., Giusti, M., Merle, M. (eds) Algebraic Geometry. Lecture Notes in Mathematics, vol 961. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071281

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  • DOI: https://doi.org/10.1007/BFb0071281

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11969-2

  • Online ISBN: 978-3-540-39367-2

  • eBook Packages: Springer Book Archive

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