On seminormal schemes

S. Greco; C. Traverso

Compositio Mathematica (1980)

  • Volume: 40, Issue: 3, page 325-365
  • ISSN: 0010-437X

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Greco, S., and Traverso, C.. "On seminormal schemes." Compositio Mathematica 40.3 (1980): 325-365. <http://eudml.org/doc/89442>.

@article{Greco1980,
author = {Greco, S., Traverso, C.},
journal = {Compositio Mathematica},
keywords = {seminormal schemes; noetherian ring; integral closure; local one- dimensional Gorenstein; Gorenstein schemes; generic projections; formal fibers},
language = {eng},
number = {3},
pages = {325-365},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {On seminormal schemes},
url = {http://eudml.org/doc/89442},
volume = {40},
year = {1980},
}

TY - JOUR
AU - Greco, S.
AU - Traverso, C.
TI - On seminormal schemes
JO - Compositio Mathematica
PY - 1980
PB - Sijthoff et Noordhoff International Publishers
VL - 40
IS - 3
SP - 325
EP - 365
LA - eng
KW - seminormal schemes; noetherian ring; integral closure; local one- dimensional Gorenstein; Gorenstein schemes; generic projections; formal fibers
UR - http://eudml.org/doc/89442
ER -

References

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  1. [1] A. Andreotti and E. Bombieri: Sugli omeomorfismi delle varietà algebriche. Ann. Sc. Norm. Sup. Pisa23 (1969) 430-450. Zbl0184.24503MR266923
  2. [2] 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
  3. [3] H. Bass: On the ubiquity of Gorenstein rings. Math. Z.82 (1963) 8-28. Zbl0112.26604MR153708
  4. [4] H. Bass and P. Murthy: Grothendieck groups and Picard groups of abelian group rings. Ann. of Math.86 (1967) 16-73. Zbl0157.08202MR219592
  5. [5] E. Bombieri: Seminormalità e singolarità ordinarie. Symp. Math.XI (1973) 205-210. Zbl0294.14015MR429874
  6. [6] N. Bourbaki: Algèbre Commutative. ch. I, II, Hermann, Paris1961. 
  7. [7] N. Bourbaki: Algèbre Commutative. ch. III, IV, Hermann, Paris1961. MR171800
  8. [8] N. Bourbaki: Algèbre Commutative. ch. V, VI, Hermann, Paris1964. MR194450
  9. [9] N. Chiarli: Sulla seminormalità di certe superfici algebriche. Atti Acc. Sc. Torino108 (1973-74) 605-611. Zbl0326.14010MR485886
  10. [10] A. Franchetta: Sulla varietà doppia della proiezione generica di una varietà algebrica non singolare. Acc. Scienze Lettere ed Arti di Palermo14 (1953-54) 1-12. 
  11. [11] S. Greco: Anelli Henseliani in Categories and Commutative Algebra. Cremonese, Roma, 1974. MR366915
  12. [12] S. Greco: Seminormalità delle varietà di Gorenstein. Atti Acc. Naz. Lincei58 (1975) 556-558. Zbl0346.14018MR422293
  13. [13] S. Greco: Two theorems on excellent rings. Nagoya Math. J.60 (1976) 139-149. Zbl0308.13010MR409452
  14. [14] S. Greco and P. Salmon: Topics in m-adic topologies. Erg. Der Math.b. 58, Springer-Verlag1971. Zbl0205.34501MR282956
  15. [15] S. Greco and N. Sankaran: On the separable and algebraic closedness of a Hensel couple in its completion. J. of Algebra39 (1976) 335-348. Zbl0332.13015MR409454
  16. [16] S. Greco and P. Valabrega: On the excellent property for strictly convergent power series rings over a complete non Archimedean valued field. Atti Acc. Sc. Torino108 (1973-74) 529-539. Zbl0332.13014MR392986
  17. [17] A. Grothendieck and J. Dieudonne: Eléments de Géométrie Algébrique I. Grund. der Math.166, Springer-Verlag1971. Zbl0203.23301
  18. [18] A. Grothendieck and J. Dieudonne: Eléments de Géométrie Algébrique II, III, IV, Publ. Math.8,..., Paris1961. Zbl0203.23301
  19. [19] J. Herzog and E. Kunz: Der kanonische Modul eines Cohen-Macaula y Rings. Lect. Notes Math.238, Springer-Verlag1971. Zbl0231.13009MR412177
  20. [20] H. Hironaka: Resolution of singularities of an algebraic variety over a field of characteristic zero. Ann. of Math.79 (1964) 109-326. Zbl0122.38603MR199184
  21. [21] F. Ischebeck: Eine dualitat zwischen Ext und Tor. J. of Algebra11 (1969) 510-531. Zbl0191.01306MR237613
  22. [22] F. Ischebeck: Zur Picard-Gruppe eines Products. Math. Z.139 (1974) 141-157. Zbl0275.14004MR401758
  23. [23] M. Marinari: Su alcune classi di anelli noetheriani che comprendono gli anelli di Gorenstein. Ann. Univ. Ferrara, Sez. VII, 19 (1974) 135-143. Zbl0296.13016MR472805
  24. [24] M. Marinari: Gorenstein sequences and Gn condition. J. of Algebra39 (1976) 349-359. Zbl0342.13010MR412170
  25. [25] E. Matlis: 1-dimensional Cohen-Macaulay rings, Lect. Notes Math.327, Springer-Verlag1973. Zbl0264.13012MR357391
  26. [26] H. Matsumura: Commutative Algebra, Benjamin, New York, 1970. Zbl0211.06501MR266911
  27. [27] J. Roberts: Generic projections of algebraic varieties. Am. J. Math.93 (1971) 191-214. Zbl0212.53801MR277530
  28. [28] P. Salmon: Sur les séries formelles restreintes. Bull. Soc. Math. France92 (1964) 385-410. Zbl0196.31101MR178010
  29. [29] P. Salmon: Singolarità e gruppo di Picard. Symp. Math.II (1968) 341-345. Zbl0186.54801MR251032
  30. [30] J.P. Serre: Géométrie algébrique et Géométrie Analytique. Ann. Inst. Fourier6 (1955) 1-42. Zbl0075.30401MR82175
  31. [31] C. Traverso: Seminormality and Picard Group. Ann. Sc. Norm. Sup. Pisa24 (1970) 585-595. Zbl0205.50501MR277542
  32. [32] W. Vasconcelos: Quasi-normal rings, Ill. J. Math14 (1970) 268-273. Zbl0188.33602MR257126
  33. [33] G. Fischer: Complex Analytic Geometry, Lect. Notes Math.538, Springer-Verlag1976. Zbl0343.32002MR430286
  34. [34] J. Frisch: Points de platitude d'un morphisme d'espaces analytiques complexes. Inv. Math.4 (1967) 118-138. Zbl0167.06803MR222336
  35. [35] R.C. Gunning and H. Rossi: Analytic functions of several complex variables, Prentice Hall Inc., 1965. Zbl0141.08601MR180696
  36. [36] H. Matsumura: Formal power series rings over polynomial rings I, Number Theory, Algebraic Geometry and Commutative Algebra in honor of Y. Akizuki, KinokuniyaTokyo1973, 511-520. Zbl0271.13015MR366909
  37. [37] R. Narasimhan: Introduction to the theory of Analytic Spaces, Lect. Notes Math.25, Springer-Verlag1966. Zbl0168.06003MR217337
  38. [38] R. Narasimhan: Imbedding of holomorphically complete complex spaces. Am. J. Math.82 (1960) 917-934. Zbl0104.05402MR148942
  39. [39] E.D. Davis: On the geometric interpretation of seminormality, Proc. AMS68 (1978) 1-5. Zbl0386.13012MR453748
  40. [40] R. Piene: Polar classes of singular varieties. Ann. Ec. Norm. Sup.4 ser., Vol 11 (1978) 247-276. Zbl0401.14007MR510551
  41. [41] P.M.H. Wilson: On blowing up conductor ideals, Math. Proc. Camb. Phil. Soc.83 (1978) 445-450. Zbl0383.14001MR463171

Citations in EuDML Documents

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  1. Mario Raimondo, On normalization of Nash varieties
  2. Nadia Chiarli, Characterizations of certain singularities of a branched covering
  3. Karl Schwede, Kevin Tucker, On the number of compatibly Frobenius split subvarieties, prime F -ideals, and log canonical centers
  4. Rahim Zaare-Nahandi, Seminormality of certain generic projections
  5. Angelo Vistoli, Incollamento di punti chiusi e gruppo fondamentale algebrico e topologico
  6. Joel Roberts, Rahim Zaare-Nahandi, Transversality of generic projections and seminormality of the image hypersurfaces
  7. William A. Adkins, Weak normality and Lipschitz saturation for ordinary singularities
  8. Caterina Cumino, Silvio Greco, Mirella Manaresi, Bertini theorems for weak normality
  9. David Rydh, Submersions and effective descent of étale morphisms

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