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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Smoothing curves in $ {\bf P}\sp 3$ with $ p\sb a=1$


Author: Carmen A. Sánchez
Journal: Proc. Amer. Math. Soc. 99 (1987), 613-616
MSC: Primary 14H45; Secondary 14C05, 14H50
DOI: https://doi.org/10.1090/S0002-9939-1987-0877026-0
MathSciNet review: 877026
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Abstract: In [3] Tannenbaum proved that every connected, reduced curve in $ {P^3}$ of arithmetic genus 0 may be smoothed. Here we prove, using results of Hartshorne and Hirschowitz [1], that every connected, reduced curve in $ {P^3}$ of arithmetic genus 1 is also smoothable.


References [Enhancements On Off] (What's this?)

  • [1] R. Hartshorne and A. Hirschowitz, Smoothing algebraic space curves, Algebraic Geometry, Proceedings Sitges 1983, Lecture Notes in Math., vol. 1124, Springer-Verlag, Berlin and New York, 1985, pp. 98-131. MR 805332 (87h:14023)
  • [2] H. Hironaka, On the arithmetic genera and the effective genera of algebraic curves, Mem. Coll. Sci. Univ. Kyoto 30 (1957), 177-195. MR 0090850 (19:881b)
  • [3] A. Tannenbaum, Degenerations of curves in $ {P^3}$, Proc. Amer. Math. Soc. 68 (1978), 6-10. MR 0457448 (56:15653)

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DOI: https://doi.org/10.1090/S0002-9939-1987-0877026-0
Article copyright: © Copyright 1987 American Mathematical Society

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