Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-28T15:00:40.190Z Has data issue: false hasContentIssue false

On certain isolated normal singularities

Published online by Cambridge University Press:  22 January 2016

Lucian Bădescu*
Affiliation:
University of Bucharest, Dept. of Mathematics
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 the following we shall fix an algebraically closed field K of arbitrary characteristic. The term variety will mean an algebraic scheme over K which is integral. In general we shall use the notations and the terminology of Éléments de Géométrie Algébrique of A. Grothendieck and J. Dieudonné. For instance, if Z is a variety and x ∈ Z is a point, then OZ, x means the local ring of Z at x and mx – the maximal ideal of 0Z, x.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

[1] Altman, A. and Kleiman, S., Introduction to Grothendieck Duality Theory, Springer Lecture Nothes in Math. (1970).CrossRefGoogle Scholar
[2] Artin, M., Some numerical criteria for contractibility of curves on an algebraic surface, Amer. J. Math:. 84 (1962), pp. 485496.Google Scholar
[3] Artin, M., On isolated rational singularities of surfaces, Amer. J. Math. 88 (1966), pp. 129136.Google Scholar
[4] Bass, H., On the ubiquity of Gorenstein rings, Math. Zeit. 82 (1963), pp. 828.CrossRefGoogle Scholar
[5] Bădescu, L., Contractions rationnelles des variétés algébriques, Annali Sc. Norm. Sup. Pisa, 27 (1973), pp. 743747.Google Scholar
[6] Bădescu, L., Contractions algébriques et applications, Revue Roum. Math. Pur. Appl. XIX, 2 (1974), pp. 143160.Google Scholar
[7] Bădescu, L. et Fiorentini, M., Criteri di semifattorialità e di fattorialità per gli anelli locali con applicazioni geometrche, Annali Mat. Pura Appl. CII (1975), pp. 211222.Google Scholar
[8] Brînzănescu, V., Asupra scufundărilor Veronese, Studii Cere. Matematice Nr. 5 (1974).Google Scholar
[9] Fiorentini, M., Esempi di anelli di Cohen-Macaulay semifattoriali che non sono di Gorenstein, Rend. Acad. Lincei, series VIII, 50, fasc. 5 (1971).Google Scholar
[10] Grothendieck, A., Séminaire de Géométrie Algébrique 1962 (SGA II), Paris.Google Scholar
[11] Grothendieck, A., et Dieudonné, J., Éléments de Géométrie Algébrique (E.G.A.), chap. I—III, 1961, Paris.Google Scholar
[12] Mumford, D., Lectures on curves on an algebraic surface, Princeton, New Jersey, 1966.Google Scholar
[13] Serre, J. P., Faisceaux algébriques cohérents (FAC), Annals Math. 61 (1955), p. 197278.Google Scholar