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Proceedings of the American Mathematical Society

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Degenerations of curves in $ P\sp{3}$


Author: Allen Tannenbaum
Journal: Proc. Amer. Math. Soc. 68 (1978), 6-10
MSC: Primary 14H20; Secondary 14D15
DOI: https://doi.org/10.1090/S0002-9939-1978-0457448-7
MathSciNet review: 0457448
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Abstract: In this paper we prove every connected, reduced curve in $ {{\mathbf{P}}^3}$ of arithmetic genus 0, may be flatly smoothed. Moreover, we give a new example of a reduced singular curve in $ {{\mathbf{P}}^3}$ which cannot be flatly smoothed.


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  • [1] A. Grothendieck, Éléments de géométrie algébrique. III, Inst. Hautes Études Sci. Publ. Math. 11 (1961).
  • [2] -, Techniques de construction et théorèmes d'existence en géométrie algébrique. IV, les schémas de Hilbert, Séminaire Bourbaki, No. 221, 1961, pp. 1-28.
  • [3] Robin Hartshorne, Connectedness of the Hilbert scheme, Inst. Hautes Études Sci. Publ. Math. 29 (1966), 5–48. MR 0213368
  • [4] C. H. Halphen, Classification des courbes gauches algébriques, Oeuvres III, Gauthier-Villars, Paris, 1921.
  • [5] Heisuke Hironaka, On the arithmetic genera and the effective genera of algebraic curves, Mem. Coll. Sci. Univ. Kyoto. Ser. A. Math. 30 (1957), 177–195. MR 0090850
  • [6] M. Noether, Zur Grundlegung der Theorie der algebraischen Raumkurven, Crelle Journal 93 (1882).
  • [7] C. Peskine and L. Szpiro, Liaison des variétés algébriques. I, Invent. Math. 26 (1974), 271–302 (French). MR 0364271, https://doi.org/10.1007/BF01425554
  • [8] Jean-Pierre Serre, Groupes algébriques et corps de classes, Publications de l’institut de mathématique de l’université de Nancago, VII. Hermann, Paris, 1959 (French). MR 0103191

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0457448-7
Article copyright: © Copyright 1978 American Mathematical Society