Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-21T05:38:30.765Z Has data issue: false hasContentIssue false
  • English
  • Français

The parametric blowing-up of two-dimensional local domains

Published online by Cambridge University Press:  24 October 2008

Peter Schenzel
Peter Schenzel
Affiliation:
Martin-Luther-Universitt, Halle-Wittenberg, DDR-4010 Halle, German Democratic Republic
Get access Rights & Permissions [Opens in a new window]

Extract

Let (A, M) be a local Noetherian integral domain of dimension two and X = Spec A. For an ideal IA the graded ring RA(I) = noIn denotes the Rees algebra of A with respect to I. The projective scheme Y = Proj RA(I) is called the blowing-up of X (resp. A) along I. Then there exists a proper mapping : YX. The preimage Z = 1(V(I)) is called the exceptional fibre. Note that induces an isomorphism

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 2 , September 1983 , pp. 217 - 228
Copyright
Copyright © Cambridge Philosophical Society 1983

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Auslander, M. and Buchsbaum, D. A.Codimension and multiplicity. Ann. of Math. 68 (1958), 625657.CrossRefGoogle Scholar
(2)Brodmann, M.Local cohomology of certain Rees- and form rings. I. J. Algebra 81 (1983), 2957.Google Scholar
(3)Faltings, G.ber Macaulayfizierung. Math. Ann. 238 (1978), 175192.Google Scholar
(4)Ferrand, D. and Raynaud, M.Fibres formelles d'un anneau local Noethrien. Ann. Sci. cole Norm. Sup. 3 (1970), 295311.CrossRefGoogle Scholar
(5)Goto, S.Blowing-up characterization for local rings. Abstracts of talks at Brandeis University, Waltham, 1981.Google Scholar
(6)Grothendieck, A.Local cohomology. Lecture Notes in Mathematics, no. 41 (Springer-Verlag, 1967).Google Scholar
(7)Huneke, C.On the symmetric and Rees algebra of an ideal generated by a d-sequence. J. Algebra 62 (1980), 268275.Google Scholar
(8)Matijevic, J. and Roberts, P.A conjecture of Nagata on graded CohenMacaulay rings. J. Math. Kyoto Univ. 14 (1974), 125128.Google Scholar
(9)Nagata, M.Local rings (Wiley-Interscience, 1962).Google Scholar
(10)Ratliff, L. J. JrTWO theorems on the prime divisors of zero in completions of local domains. Pacific J. Math. 81 (1979), 537545.Google Scholar
(11)Schenzel, P.Dualisierende Komplexe in der lokalen Algebra und Buchsbaum-Ringe. Lecture Notes in Mathematics, no. 907 (Springer-Verlag, 1982).CrossRefGoogle Scholar
(12)Schenzel, P.Regular sequences in Rees and symmetric algebras; I. Manuscripta math. 35 (1981), 173193.Google Scholar
(13)Shimoda, Y.A note on Rees algebras of two dimensional local domains. J. Math. Kyoto Univ. 19 (1979), 327333.Google Scholar
(14)Stckrad, J. and Vogel, W.Toward a theory of Buchsbaum singularities. Amer. J. Math. 100 (1978), 727746.CrossRefGoogle Scholar
(15)Valla, G.On the symmetric and Rees algebras of an ideal. Manuscripta math. 30 (1980), 239255.Google Scholar
(16)Watanabe, K., and others. On tensor products Gorenstein rings. J. Math. Kyoto Univ. 9 (1969), 413423.Google Scholar