@article{CM_1995__97_3_403_0, author = {Aberbach, Ian M. and Huneke, Craig and Trung, Ng\^o Vi\^et}, title = {Reduction numbers, {Brian\c{c}on-Skoda} theorems and the depth of {Rees} rings}, journal = {Compositio Mathematica}, pages = {403--434}, publisher = {Kluwer Academic Publishers}, volume = {97}, number = {3}, year = {1995}, mrnumber = {1353282}, zbl = {0854.13003}, language = {en}, url = {http://www.numdam.org/item/CM_1995__97_3_403_0/} }
TY - JOUR AU - Aberbach, Ian M. AU - Huneke, Craig AU - Trung, Ngô Viêt TI - Reduction numbers, Briançon-Skoda theorems and the depth of Rees rings JO - Compositio Mathematica PY - 1995 SP - 403 EP - 434 VL - 97 IS - 3 PB - Kluwer Academic Publishers UR - http://www.numdam.org/item/CM_1995__97_3_403_0/ LA - en ID - CM_1995__97_3_403_0 ER -
%0 Journal Article %A Aberbach, Ian M. %A Huneke, Craig %A Trung, Ngô Viêt %T Reduction numbers, Briançon-Skoda theorems and the depth of Rees rings %J Compositio Mathematica %D 1995 %P 403-434 %V 97 %N 3 %I Kluwer Academic Publishers %U http://www.numdam.org/item/CM_1995__97_3_403_0/ %G en %F CM_1995__97_3_403_0
Aberbach, Ian M.; Huneke, Craig; Trung, Ngô Viêt. Reduction numbers, Briançon-Skoda theorems and the depth of Rees rings. Compositio Mathematica, Volume 97 (1995) no. 3, pp. 403-434. http://www.numdam.org/item/CM_1995__97_3_403_0/
[AH] An improved Briançon-Skoda theorem with applications to the Cohen-Macaulayness of Rees rings, Math. Ann. 297 (1993) 343-369. | MR | Zbl
and :[AHH] Reduction numbers, Rees rings, and Pfaffian ideals, J. Pure Applied Alg. (to appear). | Zbl
, and :[Ar] Algebraic approximation of structures over complete local rings, Publ. Math. I.H.E.S. 36 (1969) 23-56. | Numdam | MR | Zbl
:[AN] Residual intersections in Cohen-Macaulay rings, J. Math. Kyoto Univ. 12 (1972) 307-323. | MR | Zbl
and :[BaS] A criterion for detecting m-regularity, Invent. Math. 87 (1987) 1-11. | MR | Zbl
and :[BS] Sur la clôture intégrale d'un idéal de germes de fonctions holomorphes en un point de Cn, C. R. Acad. Sci. Paris Sér A 278 (1974) 949-951. | MR | Zbl
and :[Bu] On ideals of finite homological dimension in local rings, Proc. of Camb. Phil. Soc. 64 (1968) 941-948. | MR | Zbl
:[CN] On the fibres of blowing up, J. of Indian Math. Soc. 40 (1976) 217-222. | MR | Zbl
and :[CST] Verallgemeinerte Cohen-Macaulay-Moduln, Math. Nachr. 85 (1978) 57-73. | MR | Zbl
, , and :[EG] Linear free resolutions and minimal multiplicities, J. Algebra 88 (1984) 89-133. | MR | Zbl
and :[GH] On graded rings associated with analytic deviation one ideals, Amer. J. Math. (to appear). | MR | Zbl
and :[GN1 ] Cohen-Macaulay Rees algebras of ideals having analytic deviation two (preprint). | Zbl
and :[GN2] Gorenstein graded rings associated to ideals of analytic deviation two (preprint). | Zbl
and :[GNi] Filtrations and the Gorenstein property of the associated Rees algebras (preprint). | MR | Zbl
and :[GS] On the Rees algebras of Cohen-Macaulay local rings, Lect. Notes in Pure and Applied Mathematics, vol. 68, Marcel-Dekker, New York, 1979, pp. 201-231. | MR | Zbl
and :[GW] On graded rings I, J. Math. Soc. Japan 30 (1978) 179-213. | MR | Zbl
and :[GHO] Graded rings associated to equimultiple ideals, Math. Z. 186 (1984) 531-566. | MR | Zbl
, , and :[HI] On the Gorenstein property of Rees algebras, Manu. Math. 58 (1987) 471-490. | MR | Zbl
and :[HHR] On reduction exponents of ideals with Gorenstein form ring, Proc. Edinburgh Math. Soc. (to appear). | Zbl
, , and :[HRS] On the Gorenstein property of formrings (preprint). | Zbl
, , and :[HSV1] On the arithmetic and homology of algebras of linear type, Trans. Amer. Math. Soc. 283 (1984) 661-683. | MR | Zbl
, , and :[HSV2] On the canonical module of the Rees algebra and the associated graded ring of an ideal, J. of Alg. 105 (1987) 285-302. | MR | Zbl
, , and :[HoHu1] tight closure, invariant theory, and the Briançon-Skoda theorem, J. Amer. Math. Soc. 3 (1990) 31-116. | MR | Zbl
and :[HR] Five theorems on Macaulay rings, Pac. J. of Math. 44 (1973) 147-172. | MR | Zbl
and :[HH1] Powers of ideals having small analytic deviation, Amer. J. Math. 114 (1992) 367-403. | MR | Zbl
and :[HH2] Rees algebras of ideals having small analytic deviation, Trans. Amer. Math. Soc. 339 (1993) 373-402. | MR | Zbl
and :[HM] Depth properties of Rees algebras and associated graded rings, J. Algebra 156 (1993) 259-271. | MR | Zbl
and :[Hu1] On the associated graded ring of an ideal, Illinois J. Math. 26 (1982) 121-137. | MR | Zbl
:[Hu2] The theory of d-sequences and powers of ideals, Adv. in Math. 46 (1982) 249-279. | MR | Zbl
:[I] On the Gorenstein property of Rees algebras over local rings, Nagoya Math. J. 92 (1986) 135-154. | MR | Zbl
:[JK] Castelnuovo regularity and graded rings associated to an ideal, Proc. Amer. Math. Soc. (to appear). | MR | Zbl
and :[L] Cohen-Macaulayness in graded algebras, Math. Res. Letters 1 (1994) 149-157. | MR | Zbl
:[LS] Jacobian ideals and a theorem of Briançon-Skoda, Michigan Math. J. 28 (1981) 199-222. | MR | Zbl
and :[LT] Pseudo-rational local rings and a theorem of Briançon-Skoda about integral closures of ideals, Michigan Math. J. 28 (1981) 97-116. | MR | Zbl
and :[MR] A conjecture of Nagata on graded Cohen-Macaulay rings, J. Math. Kyoto Univ. 14 (1974) 125-138. | MR | Zbl
and :[Ma] Commutative Ring Theory, Cambridge University Press, Cambridge, 1986. | MR | Zbl
:[Mu] Lectures on curves on an algebraic surface, Princeton University Press, Princeton, New Jersey, 1966. | MR | Zbl
:[Mc] Asymptotic prime divisors, Lect. Notes in Math. 1023, Springer, 1983. | MR | Zbl
:[NR] Reductions of ideals in local rings, Math. Proc. Camb. Phil. Soc. 50 (1954) 145-158. | MR | Zbl
and :[NV] The S2-closure of a Rees algebra, Results in Math. 23 (1993) 149-162. | MR | Zbl
and :[O] Castelnuovo's regularity of graded rings and modules, Hiroshima Math. J. 12 (1982) 627-644. | Zbl
:[Sa] On the associated graded ring of a local Cohen-Macaulay ring, J. Math. Kyoto Univ. 17 (1977) 19-21. | MR | Zbl
:[SS] Géométrie Algébrique et applications I, La Rabida, Travaux en Cours, vol. 22, Hermann, Paris, 1987, pp. 201-209. | Zbl
:[SUV] Cohen-Macaulay Rees algebras and degrees of polynomial relations, Math. Annalen (to appear). | MR | Zbl
, , and :[SV] The syzygies of the conormal module, Amer. J. of Math. 103 (1981) 203-224. | MR | Zbl
and :[Ta] Rees rings and associated graded rings of ideals having higher analytic deviation (preprint). | MR | Zbl
:[T1] Reduction exponents and degree bound for the defining equations of graded rings, Proc. Amer. Soc. 101 (1987) 229-234. | MR | Zbl
:[T2] Filter-regular sequences and multiplicity of blow-up rings of ideals of the principal class, J. Math. Kyoto Univ. (to appear). | MR | Zbl
:[T3] Reduction number, α-invariant, and Rees algebras of ideals having small analytic deviation, Proceedings of the Workshop on Commutative Algebra, Trieste 1992 (to appear). | Zbl
:[TI] When is the Rees algebra Cohen-Macaulay?, Comm. Algebra 17(12) (1989) 2893-2922. | MR | Zbl
and :[U] Artin-Nagata properties and reductions of ideals, Cont. Math. 159 (1994) 373-400. | MR | Zbl
:[UV] The equations of Rees algebras of ideals with linear presentation, Math. Z. 214 (1993) 79-92. | MR | Zbl
and :[VV] Form rings and regular sequences, Nagoya Math. J. 72 (1978) 91-101. | MR | Zbl
and :[Va1] On the equations of Rees algebras, J. reine angew. Math. 418 (1991) 189-218. | MR | Zbl
:[Va2] Hilbert functions, analytic spread, and Koszul homology, Cont. Math. 159 (1994) 401-422. | MR | Zbl
:[Va3] Arithmetic of Blowup Algebras (manuscript).
:[Vi] A note on the Cohen-Macaulayness of Rees algebras of filtrations, Comm. in Alg. 21 (1993) 221-229. | MR | Zbl
: