A Depth Formula for Generic Singularities and Their Weak Normality

REFERENCES

• Adkins , W. ( 1984 ). Weak normality and Lipschitz saturation for ordinary singularities . Comp. Math. 51 : 149 – 157 .
   Web of Science ®Google Scholar
• Adkins , W. , Andreotti , A. , Leahy , J. ( 1981 ). Weakly normal complex spaces . Accad. Naz. Lincei. Contributi del Cen. Interdisciplinare di Scienze Mat. 55 : 2 – 56 .
   Google Scholar
• Andreotti , A. , Norguet , F. ( 1967 ). La convexité holomorphe dans l'espace analytique des cycles d'une veriété algébrique . Ann. Scuola Norm. Sup. Pisa 21 : 31 – 82 .
   Google Scholar
• Andreotti , A. , Bombieri , E. ( 1969 ). Sugli omeomorfismi delle varietà algebriche . Ann. Scuola Nor. Sup. Pisa 23 : 430 – 450 .
   Google Scholar
• Andreotti , A. , Holm , P. ( 1977 ). Quasi Analytic and Parametric Spaces . Oslo 1976 . Netherlands : Sijthhoff and Nordhoff , pp. 13 – 97 .
   Google Scholar
• Bass , H. , Murthy , P. ( 1967 ). Grothendieck and Picard groups of abelian group rings . Ann. Math. 86 : 16 – 73 .
   Web of Science ®Google Scholar
• Bombieri , E. ( 1973 ). Seminormalità e singularità ordinarie . Symposia Mathematica XI . New York : Academic Press , pp. 205 – 210 .
   Google Scholar
• Bourbaki , N. ( 1970 ). Élèmentes de Mathèmatique, Algèbre I . Chs. 1–3 . Berlin, New York, Paris : Springer-Verlag .
   Google Scholar
• Bump , D. ( 1998 ). Algebraic Geometry . Singapore, New Jersey, London, Hog Kong : World Scientific .
   Google Scholar
• Dayton , B. H. ( 1981 ). Seminormality Implies the Chinese Remainder Thoerem . Lecture Notes in Math. Vol. 854 . New York : Springer , pp. 124 – 126 .
   Google Scholar
• Greco , S. ( 1978 ). Normal Varieties . Istituto Nazionale di Alta Matematica . Vol. IV . London, New York : Academic Press .
   Google Scholar
• Greco , S. , Traverso , C. ( 1980 ). On seminormal schemes . Comp. Math. 40 : 325 – 365 .
   Web of Science ®Google Scholar
• Grothendieck , A. ( 1967 ). Éléments de géométrie algébrique IV, Études locale des schémas et des morphismes de schémas. 4 e partie. Rédigés avec la collaboration de J. Dieodonné . Inst. Hautes Études Sci. Publ. Math. No. 32 .
   Google Scholar
• Kleiman , S. ( 1977 ). The enumerative theory of singularities . Real and Complex Singularities . Oslo 1976 . Netherlands : Sijthoff and Nordhoff , pp. 297 – 396 .
   Google Scholar
• Lipman , J. ( 1971 ). Stable ideals and Arf rings . Amer. J. Math. 93 : 649 – 685 .
   Web of Science ®Google Scholar
• Lipman , J. ( 1975 ). Relative Lipschitz saturation . Amer. J. Math. 97 ( 3 ): 791 – 813 .
   Web of Science ®Google Scholar
• Manaresi , M. ( 1980 ). Some properties of weakly normal varieties . Nagoya Math. J. 77 : 61 – 74 .
   Web of Science ®Google Scholar
• Matsumura , H. ( 1986 ). Commutative Ring Theory . Cambridge : Cambridge University Press .
   Google Scholar
• Mond , D. , Pellikaan , R. ( 1989 ). Fitting Ideals and Multiple Points of Analytic Mappings . Lecture Notes in Mathematics 1414 . New York : Springer , pp. 105 – 161 .
   Google Scholar
• Orecchia , F. ( 1975 ). Sul gruppo di Picard di certe algebre non integre . Ann. Univ. Ferrara. Sez. VII-Sc-Mat. Vol. XXI : pp. 25 – 36 .
   Google Scholar
• Orecchia , F. (1976). Sulla seminormalità de certe varietà affini riducibili. Bullettino U. M. I. (5) 13-B:588–600.
   Google Scholar
• Pham , F. ( 1970 ). Fractions Lipschitziennes et saturation de Zariski des algèbres analytiques complexes . Actes. Congres Inter. Math. Tome 2 : 649 – 654 .
   Google Scholar
• Piene , R. ( 1989 ). Private communication . 17 February, 1989. Oslo, Norway .
   Google Scholar
• Roberts , J. ( 1971 ). Generic projections of algebraic geometry . Amer. J. Math. 93 ( 1 ): 191 – 214 .
   Web of Science ®Google Scholar
• Roberts , J. ( 1975 ). Singularity subschemes and generic projections . Trans. Amer. Math. Soc. 212 : 229 – 268 .
   Web of Science ®Google Scholar
• Roberts , J. ( 1978 ). Hypersurfaces with nonsingular normalization and their double loci . J. Algebra 53 : 253 – 267 .
   Google Scholar
• Roberts , J. ( 1980 ). Some properties of double point schemes . Comp. Math. 41 : 61 – 94 .
   Web of Science ®Google Scholar
• Roberts , J. ( 1982 ). Private communication . 29 September, 1982. Minneapolis, Minnesota .
   Google Scholar
• Roberts , J. ( 1985 ). Private communication . 18 June, 1985. Minneapolis, Minnesota .
   Google Scholar
• Roberts , J. , Zaare-Nahandi , R. ( 1984 ). Transversality of generic projections and seminormality of the image hypersurfaces . Comp. Math. 52 : 211 – 220 .
   Google Scholar
• Salmon , P. ( 1969 ). Singolarità e gruppo di Picard , Symposia Mathematica II . New York : Acedemic Press , pp. 341 – 345 .
   Google Scholar
• Salmon , P. , Zaare-Nahandi , R. ( 2005 ). Ideals of minors defining generic singularities and their Gröbner bases . Comm. Algebra 33 ( 8 ): 2725 – 2747 .
   Web of Science ®Google Scholar
• Shafarevich , I. ( 1977 ). Basic Algebraic Geomery . Berlin, Heidelberg, New York : Springer-Verlag .
   Google Scholar
• Traverso , C. ( 1970 ). Seminormality and Picard group . Annali della Scuola Norm. Sup. Pisa 24 : 585 – 595 .
   Google Scholar
• Zaare-Nahandi , R. ( 1984 ). Seminormality of certain generic projections . Comp. Math. 52 : 245 – 274 .
   Web of Science ®Google Scholar
• Zaare-Nahandi , R. , Zaare-Nahandi , R. ( 2004 ). The minimal free resolution of a class of square-free monomial ideals . J. Pure Appl. Algebra 189 ( 1–3 ): 263 – 278 .
   Web of Science ®Google Scholar
• Zariski , O. , Samuel , P. ( 1958 ). Commutative Algebra . Vol. I . New York : Springer-Verlag .
   Google Scholar
• Communicated by R. Piene.
   Google Scholar