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Enumerative Geometry pp 189–214Cite as

On Schubert's degenerations of cuspidal plane cubics

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1436))

Abstract

In this paper we prove that the variety of complete cuspidal cubics is smooth in codimension one and that there are no first order degenerations other than Schubert's 13. We also establish a number of properties of cuspidal cubics that give a geometric understanding of the “Stammzahlen” tables of Schubert.

The authors were partially supported by the CAICYT and DGICYT

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References

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  • Miret, J. M.; Xambó, S. [1987], Geometry of complete cuspidal plane cubics, Preprint Univ. of Barcelona, 1987 (to appear in the Proceedings of the Trento Conference on “Algebraic curves and Projective Geometry”, March 1988)

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  • Sacchiero, G. [1984], Numeri caratteristici delle cubiche piane cuspidale, Preprint Univ. di Roma II (1984).

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  • Schubert, H. C. H. [1879], Kalkül der abzählenden der Geometrie, Teubner, Leipzig, 1879 (reprinted by Springer-Verlag, 1979).

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  • Xambó Descamps, S. [1987], The method of degenerations in enumerative geometry, Preprint Univ. of Barcelona, 1987.

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Authors and Affiliations

  1. Departament d'Àlgebra i Geometria, Universitat de Barcelona, Gran Via, 585, 08007, Barcelona, Spain

    J. M. Miret & S. Xambó Descamps

Authors
  1. J. M. Miret
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  2. S. Xambó Descamps
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Sebastian Xambó-Descamps

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© 1990 Springer-Verlag

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Miret, J.M., Xambó Descamps, S. (1990). On Schubert's degenerations of cuspidal plane cubics. In: Xambó-Descamps, S. (eds) Enumerative Geometry. Lecture Notes in Mathematics, vol 1436. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084046

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  • DOI: https://doi.org/10.1007/BFb0084046

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52811-1

  • Online ISBN: 978-3-540-47154-7

  • eBook Packages: Springer Book Archive

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