No rational nonsingular quartic curve 𝒞 4 ⊂ ℙ 3 can be set-theoretic complete intersection on a cubic surface

P. C. Craighero; R. Gattazzo

Rendiconti del Seminario Matematico della Università di Padova (1989)

  • Volume: 81, page 171-192
  • ISSN: 0041-8994

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Craighero, P. C., and Gattazzo, R.. "No rational nonsingular quartic curve $\mathcal {C}_4 \subset \mathbb {P}^3$ can be set-theoretic complete intersection on a cubic surface." Rendiconti del Seminario Matematico della Università di Padova 81 (1989): 171-192. <http://eudml.org/doc/108133>.

@article{Craighero1989,
author = {Craighero, P. C., Gattazzo, R.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {quartic curves; set-theoretic complete intersections},
language = {eng},
pages = {171-192},
publisher = {Seminario Matematico of the University of Padua},
title = {No rational nonsingular quartic curve $\mathcal \{C\}_4 \subset \mathbb \{P\}^3$ can be set-theoretic complete intersection on a cubic surface},
url = {http://eudml.org/doc/108133},
volume = {81},
year = {1989},
}

TY - JOUR
AU - Craighero, P. C.
AU - Gattazzo, R.
TI - No rational nonsingular quartic curve $\mathcal {C}_4 \subset \mathbb {P}^3$ can be set-theoretic complete intersection on a cubic surface
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1989
PB - Seminario Matematico of the University of Padua
VL - 81
SP - 171
EP - 192
LA - eng
KW - quartic curves; set-theoretic complete intersections
UR - http://eudml.org/doc/108133
ER -

References

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  1. [H] R. Hartshorne, Algebraic Geometry, Springer, Berlin (1977). Zbl0367.14001MR463157
  2. [C] P.C. Craighero, Una osservazione sulla curva di Cremona di P3: C = (λμ3, λ3μ, λ4, μ4), Rend. Sem. Mat. Univ. Padova, 65 (1981), pp. 177-190. Zbl0492.14020
  3. [C-G] P.C. Craighero - R. Gattazzo, The curve C = (λ4, λ3μ, λμ3, μ4) ⊂ P3 is not set-theoretic complete intersection of two quartic surfaces, Rend. Sem. Mat. Univ. Padova, 76 (1986), pp. 177-200. Zbl0613.14025
  4. [G] D. Gallarati, Appunti di Geometria, Di Stefano, Genova (1969). 
  5. [J] D.B. Jaffe, Space curves which are the intersection of a cone with another surface, to appear in Duke Math. Journal. Zbl0677.14011MR975125
  6. [K] E. Kunz, Einfuhrung in die Kommutative Algebra und Algebraische Geometrie, vieweg, Wiesbaden (1979). Zbl0432.13001MR562105
  7. [R] L. Robbiano, Some properties of complete intersection in « good » projective varieties, Nagoya Math. J., 61 (1976), pp. 103-111. Zbl0309.14043MR409467
  8. [S1] E. Stagnaro, Le superficie cubiche di P3 a curve sottoinsieme intersezione completa, Atti Acc. Ligure Sc. Arti, 36 (1975), pp. 138-148. Zbl0363.14014MR360606
  9. [S2] E. Stagnaro, Sulle curve razionali non singolari di ordine 4 di P3, Rend. Acc. Naz. Scienze detta dei XL, Memorie di Matematica, 101, (6) VII (1983), pp. 51-88. Zbl0545.14025

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