Bertini theorems for weak normality

Caterina Cumino; Silvio Greco; Mirella Manaresi

Compositio Mathematica (1983)

  • Volume: 48, Issue: 3, page 351-362
  • ISSN: 0010-437X

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Cumino, Caterina, Greco, Silvio, and Manaresi, Mirella. "Bertini theorems for weak normality." Compositio Mathematica 48.3 (1983): 351-362. <http://eudml.org/doc/89598>.

@article{Cumino1983,
author = {Cumino, Caterina, Greco, Silvio, Manaresi, Mirella},
journal = {Compositio Mathematica},
keywords = {seminormal variety; weakly normal variety; general hyperplane section; local Bertini theorem; weak normalization; seminormalization},
language = {eng},
number = {3},
pages = {351-362},
publisher = {Martinus Nijhoff Publishers},
title = {Bertini theorems for weak normality},
url = {http://eudml.org/doc/89598},
volume = {48},
year = {1983},
}

TY - JOUR
AU - Cumino, Caterina
AU - Greco, Silvio
AU - Manaresi, Mirella
TI - Bertini theorems for weak normality
JO - Compositio Mathematica
PY - 1983
PB - Martinus Nijhoff Publishers
VL - 48
IS - 3
SP - 351
EP - 362
LA - eng
KW - seminormal variety; weakly normal variety; general hyperplane section; local Bertini theorem; weak normalization; seminormalization
UR - http://eudml.org/doc/89598
ER -

References

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  1. [1] W. Adkins, A., Andreotti and J. Leahy: Weakly normal complex spaces. Atti Acc. Naz. Lincei (1981). Zbl0612.32010MR695003
  2. [2] W. Adkins and J. Leahy: A topological criterion for local optimality of weakly normal complex spaces. Math. Ann.243 (1979) 115-123. Zbl0436.32008MR543721
  3. [3] A. Andreotti and E. Bombieri: Sugli omeomorfismi delle varietà algebriche. Ann. Sc. Norm. Sup. Pisa23 (1969) 430-450. Zbl0184.24503MR266923
  4. [4] A. Andreotti and F. Norguet: La convexité holomorphe dans l'espace analytique des cycles d'une variété algébrique. Ann. Sc. Norm. Sup. Pisa21 (1967) 31-82. Zbl0176.04001MR239118
  5. [5] C. Cumino, S. Greco and M. Manaresi: Normalité faible et sections hyperplanes. C.R. Acad. Sc. Paris, 293 Série I (1981) 689-692. Zbl0485.14002MR650537
  6. [6] C. Cumino and M. Manaresi: On the singularities of weakly normal varieties. Manuscripta Math.33 (1981) 283-313. Zbl0471.14016MR612614
  7. [7] H. Flenner: Die Sätze von Bertini für lokale Ringe. Math. Ann.229 (1977) 97-111. Zbl0398.13013MR460317
  8. [8] S. Greco and C. Traverso: On seminormal schemes. Compositio Math.40 (1980) 325-365. Zbl0412.14024MR571055
  9. [9] A. Grothendieck and J. Dieudonne: Eléments de Géométrie Algébrique II, Publ. Math.8, Paris1961. Zbl0118.36206
  10. [10] A. Grothendieck and J. Dieudonne: Eléments de Géométrie Algébrique I. Grund. der Math.166, Springer-Verlag1971. Zbl0203.23301
  11. [11] J. Herzog and E. Kunz: Der kanonische Modul eines Cohen-Macaulay Rings. Lect. Notes Math.238, Springer-Verlag1971. Zbl0231.13009MR412177
  12. [12] M. Manaresi: Some properties of weakly normal varieties. Nagoya Math. J.77 (1980) 61-74. Zbl0403.14001MR556308
  13. [13] A. Ooishi: On seminormal rings (general survey). Lect. Notes RIMS Kyoto Univ.374 (1980) 1-17. 
  14. [14] A. Ooishi: Notes on graded seminormal and weakly normal rings. (preprint). 
  15. [15] P. Samuel: Méthodes d'Algébre abstraite en Géométrie Algébrique. Erg. der Math.Springer-Verlag1971. Zbl0067.38904
  16. [16] C. Traverso: Seminormality and Picard group. Ann. Sc. Norm. Sup. Pisa24 (1970) 585-595. Zbl0205.50501MR277542
  17. [17] O. Zariski and P. Samuel: Commutative Algebra II. Van Nostrand1960. Zbl0121.27801MR120249

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