Smoothing curves in $\textbf {P}^ 3$ with $p_ a=1$
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- by Carmen A. Sánchez PDF
- Proc. Amer. Math. Soc. 99 (1987), 613-616 Request permission
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
- R. Hartshorne and A. Hirschowitz, Smoothing algebraic space curves, Algebraic geometry, Sitges (Barcelona), 1983, Lecture Notes in Math., vol. 1124, Springer, Berlin, 1985, pp. 98–131. MR 805332, DOI 10.1007/BFb0074998
- 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 90850, DOI 10.1215/kjm/1250777055
- Allen Tannenbaum, Degenerations of curves in $P^{3}$, Proc. Amer. Math. Soc. 68 (1978), no. 1, 6–10. MR 457448, DOI 10.1090/S0002-9939-1978-0457448-7
Additional Information
- © Copyright 1987 American Mathematical Society
- 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