Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-28T15:47:43.286Z Has data issue: false hasContentIssue false
  • English
  • Français

Some properties of weakly normal varieties*)

Published online by Cambridge University Press:  22 January 2016

Mirella Manaresi
Mirella Manaresi*
Affiliation:
Istituto di Geometria, dell’Università di Bologna, P. za di Porta S. Donato, 5, 40100 Bologna, Italy
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we give a new characterization of weak normalization and we use it to discuss some questions about weakly normal varieties formulated by A. Andreotti and E. Bombieri in [1] and studied by S. Greco and C. Traverso in [8] for seminormality.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 77 , February 1980 , pp. 61 - 74
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1980

Footnotes

*)

This research was supported by GNSAGA of C.N.R.

References

[1] Andreotti, A. and Bombieri, E., Sugli omeomorfismi delle varietà algebriche. Ann. Scuola Norm. Sup. Pisa 23 (1969), 430–450.Google Scholar
[2] Bombieri, E., Seminormalità e singolarità ordinarie. Symp. Math. XI (1973), 205–210.Google Scholar
[3] Bourbaki, N., Algèbre Commutative. Hermann, Paris, 1961.Google Scholar
[4] Davis, E., On the geometric interpretation of seminormality. Proc. Amer. Math. Soc. 68 (1978), 1–5.Google Scholar
[5] Fossum, R., The divisor class group of a Krull domain. Erg. der Math., b. 74, Springer Verlag, 1973.Google Scholar
[6] Greco, S., Two theorems on excellent rings. Nagoya Math. J. 60 (1976), 139–149.Google Scholar
[7] Greco, S. and Sankaran, N., On the separable and algebraic closedness of a Hensel couple in its completion. J. of Algebra 39 (1976), 335–348.Google Scholar
[8] Greco, S. and Traverso, C., On seminormal schemes, to appear on Compositio Math.Google Scholar
[9] Grothendieck, A. and Dieudonné, J., Eléments de Géométrie Algébrique I, Grund. der Math. b. 166, Springer Verlag, 1971.Google Scholar
[10] Grothendieck, A., Eléments de Géométrie Algébrique IV, Publ. Math. I.H.E.S. n. 24, Paris 1965.Google Scholar
[11] Manaresi, M., Una caratterizzazione della seminormalizzazione, Boll. Un. Mat. Ital, (5) 15-A (1978), 205–213.Google Scholar
[12] Marot, J., Sur les anneaux de séries formelles restreintes, to appear.Google Scholar
[13] Matsumura, H., Commutative Algebra, W.A. Benjamin Inc., New York, 1970.Google Scholar
[14] Serre, J. P., Géométrie Algébrique et Géométrie Analytique, Ann. 1st. Fourier 6 (1955), 1–42.Google Scholar
[15] Traverso, C., Seminormality and Picard group, Ann. Scuola Norm. Sup. Pisa 24 (1970), 585–595.Google Scholar
[16] Valabrega, P., On two-dimensional regular local rings and a lifting problem, Ann. Scuola Norm. Sup. Pisa 27 (1973), 787–807.Google Scholar