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Some properties of complete intersections in “good” projective varieties

Published online by Cambridge University Press:  22 January 2016

Lorenzo Robbiano
Lorenzo Robbiano*
Affiliation:
Università de Genova
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In [10] it was proved that, if X denotes a non singular surface which is a complete intersection in (k an algebraically closed field of characteristic 0) and C an irreducible curve on X, which is a set-theoretic complete intersection in X, then C is actually a complete intersection in X; the key point was to show that Pic (X) modulo the subgroup generated by the class of is torsion-free.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 61 , July 1976 , pp. 103 - 111
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

[1] Danilov, V. I.: Rings with a discrete group of divisor classes. Math. USSR-Sb. 12 (1970), p. 368–386.Google Scholar
[2] Danilov, V. I.: On rings with a discrete divisor class group. Math. USSR-Sb. 17 (1972), p. 228–236.Google Scholar
[3] Fossum, R. M.: The divisor class group of a Krull domain. Ergebnisse der Mathematik und ihrer Grenzgebiete Bd. 74 Berlin-Heidelberg-New York Springer 1973.Google Scholar
[4] Grothendieck, A. and Dieudonné, J.: Eléments de Géométrie Algébrique (EGA IV) Publ. Math. I.H.E.S. (1964–1967).Google Scholar
[5] Grothendieck, A.: Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA 2) North-Holland Publ. Amsterdam (1962).Google Scholar
[6] Grothendieck, A.: Local cohomology. Lecture Notes in Math. 41 Springer (1967).Google Scholar
[7] Hartshorne, R. and Ogus, A.: On the f actoriality of local rings of small embedding codimension. Communications in Algebra 1 (1974).Google Scholar
[8] Hartshorne, R.: Cohomological dimension of algebraic varieties. Annals of Math. 88 (1968), p. 403–450.Google Scholar
[9] Hartshorne, R.: Topological conditions for smoothing algebraic singularities. Topology 13 (1974), p. 241–253.Google Scholar
[10] Robbiano, L.: A problem of complete intersections. Nagoya Math. J. 52 (1973), p. 129–132.Google Scholar
[11] Salmon, P.: Su un problema posto da P. Samuel. Rend. Accad. Naz. Lincei Sez VIII vol. XL, fasc. 5 (1966), p. 801–803.Google Scholar
[12] Samuel, P.: On unique factorization domains. Illinois J. Math. 5 (1961), p. 1–17.Google Scholar
[13] Storch, U.: Fastfaktorielle Ringe. Schriftenreihe des Math. Inst. (Münster) Heft 36 (1967).Google Scholar