31
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Local singularities. filtrations and tangential flatness

Pages 2785-2808 | Received 01 Jan 1998, Published online: 27 Jun 2007

References

  • Artin , M. 1976 . Lectures on deformations of singularities , Bombay : Tata Institute of Fundamental Research .
  • Bennett , B.M. 1970 . On the characteristic functions of a local ring . Ann. Math , 91 : 25 – 87 .
  • Fulton , W. 1984 . Intersection theory , Berlin : Springer . Ergebnisse, 3. Folge, Band 2
  • Grothendieck , A. and Dieudonné , J. 1964 . “ Étude locale des schemas et des mcrphismes de schemas ” . In Publ. Math. IHES Vol. 20 , 24, (1965), 28,(1966), 32,(1967)
  • Herzog , B. 1990 . Lech-Hironaka inequalities for flat couples of local rings . manuscripta math , 68 : 351 – 371 .
  • Herzog , B. 1991 . Local singularities such that all deformations are tangentially flat . Trans. Amer. Math. Soc , 324 : 555 – 601 .
  • Herzog , B. 1994 . “ Lecture Notes Math ” . In Kodaira-Spencer maps in local algebra , Vol. 1597 , Springer .
  • Hironaka , H. 1964 . Resolution of singularities of an algebraic variety over a field of charac-teristic zero . Annals of Math , 79 : 109 – 326 .
  • Hironaka , H. 1970 . Certain numerical characters of singularities . J. Math. Kyoto Univ , 10 : 151 – 187 .
  • Jahnel , J. 1991 . Tangentiale Flachheit und Lech-Hironaka-Ungleichungen , Edited by: Jena , S. Vol. 94 , Doktorarbeit .
  • Jahnel , J. 1995 . Lech's conjecture on deformations of singularities and second Harrison cohomology . J. London Math. Soc , 51 : 27 – 40 .
  • Larfeldt , T. and Lech , C. 1981 . Analytic ramifications and flat couples of local rings . Ada Math , 146 : 201 – 208 .
  • Lech , C. 1958 . Note on multiplicities of ideals . Ark. for mat , 4 : 63 – 86 . 62
  • Lech , C. 1964 . Inequalities related to certain couples of local rings . Ada Math , 112 : 69 – 89 .
  • Matsumura , H. 1986 . Commutative ring theory , Cambridge Univ. Press .
  • Singh , B. 1974 . Effect of a permissible blowing up on the local Hilbert functions . Invent. Math , 26 : 201 – 212 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.