Reduction numbers, Briançon-Skoda theorems and the depth of Rees rings
Compositio Mathematica, Tome 97 (1995) no. 3, p. 403-434
@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 con-Skoda theorems and the depth of Rees rings},
     journal = {Compositio Mathematica},
     publisher = {Kluwer Academic Publishers},
     volume = {97},
     number = {3},
     year = {1995},
     pages = {403-434},
     zbl = {0854.13003},
     mrnumber = {1353282},
     language = {en},
     url = {http://www.numdam.org/item/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, Tome 97 (1995) no. 3, pp. 403-434. http://www.numdam.org/item/CM_1995__97_3_403_0/

[AH] Aberbach I. and Huneke, C.: An improved Briançon-Skoda theorem with applications to the Cohen-Macaulayness of Rees rings, Math. Ann. 297 (1993) 343-369. | MR 1241812 | Zbl 0788.13001

[AHH] Aberbach, I.M., Huckaba, S. and Huneke, C.: Reduction numbers, Rees rings, and Pfaffian ideals, J. Pure Applied Alg. (to appear). | Zbl 0838.13003

[Ar] Artin, M.: Algebraic approximation of structures over complete local rings, Publ. Math. I.H.E.S. 36 (1969) 23-56. | Numdam | MR 268188 | Zbl 0181.48802

[AN] Artin, M. and Nagata, M.: Residual intersections in Cohen-Macaulay rings, J. Math. Kyoto Univ. 12 (1972) 307-323. | MR 301006 | Zbl 0263.14019

[BaS] Bayer, D. and Stillman, M.: A criterion for detecting m-regularity, Invent. Math. 87 (1987) 1-11. | MR 862710 | Zbl 0625.13003

[BS] Briançon, J. and Skoda, H.: 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 340642 | Zbl 0307.32007

[Bu] Burch, L.: On ideals of finite homological dimension in local rings, Proc. of Camb. Phil. Soc. 64 (1968) 941-948. | MR 229634 | Zbl 0172.32302

[CN] Cowsik, R.C. and Nori, M.V.: On the fibres of blowing up, J. of Indian Math. Soc. 40 (1976) 217-222. | MR 572990 | Zbl 0437.14028

[CST] Cuong, N.T., Schenzel, P., and Trung, N.V.: Verallgemeinerte Cohen-Macaulay-Moduln, Math. Nachr. 85 (1978) 57-73. | MR 517641 | Zbl 0398.13014

[EG] Eisenbud, D. and Goto, S.: Linear free resolutions and minimal multiplicities, J. Algebra 88 (1984) 89-133. | MR 741934 | Zbl 0531.13015

[GH] Goto, S. and Huckaba, S.: On graded rings associated with analytic deviation one ideals, Amer. J. Math. (to appear). | MR 1287943 | Zbl 0803.13002

[GN1 ] Goto, S. and Nakamura, Y.: Cohen-Macaulay Rees algebras of ideals having analytic deviation two (preprint). | Zbl 0812.13003

[GN2] Goto, S. and Nakamura, Y.: Gorenstein graded rings associated to ideals of analytic deviation two (preprint). | Zbl 0848.13005

[GNi] Goto, S. and Nishida, K.: Filtrations and the Gorenstein property of the associated Rees algebras (preprint). | MR 1197521 | Zbl 0812.13016

[GS] Goto, S. and Shimoda, Y.: 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 655805 | Zbl 0482.13011

[GW] Goto, S. and Watanabe, K.: On graded rings I, J. Math. Soc. Japan 30 (1978) 179-213. | MR 494707 | Zbl 0371.13017

[GHO] Grothe, A., Herrmann, M., and Orbanz, U.: Graded rings associated to equimultiple ideals, Math. Z. 186 (1984) 531-566. | MR 744964 | Zbl 0541.13010

[HI] Herrmann, M. and Ikeda, S.: On the Gorenstein property of Rees algebras, Manu. Math. 58 (1987) 471-490. | MR 915998 | Zbl 0641.13013

[HHR] Herrmann, M., Huneke, C., and Ribbe, J.: On reduction exponents of ideals with Gorenstein form ring, Proc. Edinburgh Math. Soc. (to appear). | Zbl 0842.13001

[HRS] Herrmann, M., Ribbe, J., and Schenzel, P.: On the Gorenstein property of formrings (preprint). | Zbl 0797.13001

[HSV1] Herzog, J., Simis, A., and Vasconcelos, W.V.: On the arithmetic and homology of algebras of linear type, Trans. Amer. Math. Soc. 283 (1984) 661-683. | MR 737891 | Zbl 0541.13005

[HSV2] Herzog, J., Simis, A., and Vasconcelos, W.V.: On the canonical module of the Rees algebra and the associated graded ring of an ideal, J. of Alg. 105 (1987) 285-302. | MR 873664 | Zbl 0613.13007

[HoHu1] Hochster M. and Huneke, C.: tight closure, invariant theory, and the Briançon-Skoda theorem, J. Amer. Math. Soc. 3 (1990) 31-116. | MR 1017784 | Zbl 0701.13002

[HR] Hochster, M. and Ratliff, L.J., Jr.: Five theorems on Macaulay rings, Pac. J. of Math. 44 (1973) 147-172. | MR 314834 | Zbl 0239.13016

[HH1] Huckaba, S. and Huneke, C.: Powers of ideals having small analytic deviation, Amer. J. Math. 114 (1992) 367-403. | MR 1156570 | Zbl 0758.13001

[HH2] Huckaba, S. and Huneke, C.: Rees algebras of ideals having small analytic deviation, Trans. Amer. Math. Soc. 339 (1993) 373-402. | MR 1123455 | Zbl 0813.13009

[HM] Huckaba, S. and Marley, T.: Depth properties of Rees algebras and associated graded rings, J. Algebra 156 (1993) 259-271. | MR 1213797 | Zbl 0813.13010

[Hu1] Huneke, C.: On the associated graded ring of an ideal, Illinois J. Math. 26 (1982) 121-137. | MR 638557 | Zbl 0479.13008

[Hu2] Huneke, C.: The theory of d-sequences and powers of ideals, Adv. in Math. 46 (1982) 249-279. | MR 683201 | Zbl 0505.13004

[I] Ikeda, S.: On the Gorenstein property of Rees algebras over local rings, Nagoya Math. J. 92 (1986) 135-154. | MR 846135 | Zbl 0585.13014

[JK] Johnston, B. and Katz, D.: Castelnuovo regularity and graded rings associated to an ideal, Proc. Amer. Math. Soc. (to appear). | MR 1231300 | Zbl 0826.13014

[L] Lipman, J.: Cohen-Macaulayness in graded algebras, Math. Res. Letters 1 (1994) 149-157. | MR 1266753 | Zbl 0844.13006

[LS] Lipman, J. and Sathaye, A.: Jacobian ideals and a theorem of Briançon-Skoda, Michigan Math. J. 28 (1981) 199-222. | MR 616270 | Zbl 0438.13019

[LT] Lipman, J. and Teissier, B.: Pseudo-rational local rings and a theorem of Briançon-Skoda about integral closures of ideals, Michigan Math. J. 28 (1981) 97-116. | MR 600418 | Zbl 0464.13005

[MR] Matijevic, J. and Roberts, P.: A conjecture of Nagata on graded Cohen-Macaulay rings, J. Math. Kyoto Univ. 14 (1974) 125-138. | MR 340243 | Zbl 0278.13013

[Ma] Matsumura, H.: Commutative Ring Theory, Cambridge University Press, Cambridge, 1986. | MR 879273 | Zbl 0603.13001

[Mu] Mumford, D.: Lectures on curves on an algebraic surface, Princeton University Press, Princeton, New Jersey, 1966. | MR 209285 | Zbl 0187.42701

[Mc] Mcadam, S.: Asymptotic prime divisors, Lect. Notes in Math. 1023, Springer, 1983. | MR 722609 | Zbl 0529.13001

[NR] Northcott, S. and Rees, D.: Reductions of ideals in local rings, Math. Proc. Camb. Phil. Soc. 50 (1954) 145-158. | MR 59889 | Zbl 0057.02601

[NV] Noh, S. and Vasconcelos, W.: The S2-closure of a Rees algebra, Results in Math. 23 (1993) 149-162. | MR 1205761 | Zbl 0777.13006

[O] Oiishi, A.: Castelnuovo's regularity of graded rings and modules, Hiroshima Math. J. 12 (1982) 627-644. | Zbl 0557.13007

[Sa] Sally, J.: On the associated graded ring of a local Cohen-Macaulay ring, J. Math. Kyoto Univ. 17 (1977) 19-21. | MR 450259 | Zbl 0353.13017

[SS] Sancho De Salas, J.B.: Géométrie Algébrique et applications I, La Rabida, Travaux en Cours, vol. 22, Hermann, Paris, 1987, pp. 201-209. | Zbl 0625.14025

[SUV] Simis, A., Ulrich, B., and Vasconcelos, W.: Cohen-Macaulay Rees algebras and degrees of polynomial relations, Math. Annalen (to appear). | MR 1324518 | Zbl 0819.13003

[SV] Simis, A. and Vasconcelos, W.V.: The syzygies of the conormal module, Amer. J. of Math. 103 (1981) 203-224. | MR 610474 | Zbl 0467.13009

[Ta] Tang, Z.: Rees rings and associated graded rings of ideals having higher analytic deviation (preprint). | MR 1285714 | Zbl 0803.13003

[T1] Trung, N.V.: Reduction exponents and degree bound for the defining equations of graded rings, Proc. Amer. Soc. 101 (1987) 229-234. | MR 902533 | Zbl 0641.13016

[T2] Trung, N.V.: Filter-regular sequences and multiplicity of blow-up rings of ideals of the principal class, J. Math. Kyoto Univ. (to appear). | MR 1239084 | Zbl 0816.13020

[T3] Trung, N.V.: 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 0927.13004

[TI] Trung, N.V. and Ikeda, S.: When is the Rees algebra Cohen-Macaulay?, Comm. Algebra 17(12) (1989) 2893-2922. | MR 1030601 | Zbl 0696.13015

[U] Ulrich, B.: Artin-Nagata properties and reductions of ideals, Cont. Math. 159 (1994) 373-400. | MR 1266194 | Zbl 0821.13008

[UV] Ulrich, B. and Vasconcelos, W.V.: The equations of Rees algebras of ideals with linear presentation, Math. Z. 214 (1993) 79-92. | MR 1234599 | Zbl 0789.13002

[VV] Valabrega, P. and Valla, G.: Form rings and regular sequences, Nagoya Math. J. 72 (1978) 91-101. | MR 514892 | Zbl 0362.13007

[Va1] Vasconcelos, W.V.: On the equations of Rees algebras, J. reine angew. Math. 418 (1991) 189-218. | MR 1111206 | Zbl 0727.13002

[Va2] Vasconcelos, W.: Hilbert functions, analytic spread, and Koszul homology, Cont. Math. 159 (1994) 401-422. | MR 1266195 | Zbl 0803.13012

[Va3] Vasconcelos, W.: Arithmetic of Blowup Algebras (manuscript).

[Vi] Viêt, D.Q.: A note on the Cohen-Macaulayness of Rees algebras of filtrations, Comm. in Alg. 21 (1993) 221-229. | MR 1194556 | Zbl 0772.13002