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A note on the discriminant of a space curve

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Abstract

The notion of afree divisor was introduced by K. Saito, who also proved that the discriminant in the semi-universal deformation of an isolated complete intersection is such a free fivisor. In this note we show that the discriminant of the semi-universal deformation of areduced space curve also has this property.

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References

  • [B-G] Buchweitz, R.; Greuel, G.-M. The Milnor number and deformations of complex curve singularities. Inv. Math.58 (1980), 241–281

    Article  MATH  MathSciNet  Google Scholar 

  • [Buch] Buchweitz, R.: Contributions à la théorie des singularités. Thesis Paris VII 1981

  • [Bur] Burch, L.: On ideals of finite homological dimension in local rings. Proc. Cambr. Phil. Soc.64 (1968), 941–948

    Article  MATH  MathSciNet  Google Scholar 

  • [B-C] Behnke, K.; Christophersen, J.: Hyperplane sections and obstructions (rational surface singularities). Comp. Math.77 (1991), 233–268

    MathSciNet  Google Scholar 

  • [Da] J. Damon;Higher Multiplicities and Almost free Divisors and Complete Insersections, Preprint 1992

  • [D-M] J. Damon and D. Mond;A-codimension and the vanishing topology of discriminants, Inv. Math.106, (1991), 217–242

    Article  MATH  MathSciNet  Google Scholar 

  • [Gr] Grauert, H.: Über die Deformationen isolierter Singularitäten analytischer Mengen. Inv. Math.15 (1972), 171–198

    Article  MATH  MathSciNet  Google Scholar 

  • [He] Herzog, J.: Deformationen von Cohen-Macaulay Algebren. J. f. Reine u. Angew. Math.318 (1980), 83–105

    MATH  MathSciNet  Google Scholar 

  • [Hu] Huneke, C.: The koszul homology of an ideal. Adv. Math.56 (1985), 295–318

    Article  MATH  MathSciNet  Google Scholar 

  • [J-S1] de Jong, T.; van Straten, D.: On the base space of a semi-universal deformation of rational quadruple points. Ann. Math.134 (1991), 653–678

    Article  Google Scholar 

  • [J-S2] de Jong, T.; van Straten, D.: Deformations of the normalization of hypersurfaces Math. Ann.288 (1990), 527–547

    Article  MATH  MathSciNet  Google Scholar 

  • [L] Looijenga, E: Isolated singular points on complete intersections. London Math. Soc. Lecture Notes Series77, Cambridge University Press, 1984

  • [P] Palamodov, V.: Deformations of complex spaces. In: Several complex variables IV, Encyclopaedia of Math. Sciences; eds: Gindikin & Khenkin, Springer Verlag, Berlin & 1990

    Google Scholar 

  • [Sa] Saito, K.: Theory of logarithmic differential forms and logarithmic vector fields. J. Fac. Sci. Univ. Tokyo Sect. 1A Math.27 (1980), 265–291

    MATH  Google Scholar 

  • [Sch] Schaps, M.: Deformations of Cohen-Macaulay schemes of codimension 2 and non-singular deformations of space curves. Am. J. Math.99 (1977), 669–684

    Article  MATH  MathSciNet  Google Scholar 

  • [S-V] Simis, A.; Vasconcelos, W.: The syzygies of the conormal module. Am. J. Math.103 (1980), 203–224

    Article  MathSciNet  Google Scholar 

  • [Tei] Teissier, B.: The hunting of invariants in the geometry of discriminants. In: Real and complex singularities. (Ed. by P. Holme) Sythoft & Noordhoff Int. Publ. Alphen a/d. Rijn, (1978)

    Google Scholar 

  • [Ter] Terao, H.: The exponents of a free hypersurface. In: Singularities. Proc. Symp. Pure Math., Vol.40, Part 2, p. 561–566

  • [Wah] Wahl, J.: Smoothings of normal surface singularities. Topology, Vol.20 (1981), 219–246

    Article  MATH  MathSciNet  Google Scholar 

  • [Wal] Waldi, R.: Deformationen von Gorenstein Singularitäten der Kodimension 3. Math. Ann.242 (1979), 201–208

    Article  MATH  MathSciNet  Google Scholar 

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  1. Mathematisches Institut, Heinrich-Heine-Universität, Universitätsstraße 1, 40225, Düsseldorf

    D. van Straten

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  1. D. van Straten
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van Straten, D. A note on the discriminant of a space curve. Manuscripta Math 87, 167–177 (1995). https://doi.org/10.1007/BF02570469

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  • DOI: https://doi.org/10.1007/BF02570469

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