On Burch's inequality and a reduction system of a filtration
Authors:
Y. Kinoshita, K. Nishida, Y. Yamanaka and A. Yoneda
Journal:
Proc. Amer. Math. Soc. 134 (2006), 34373444
MSC (2000):
Primary 13A02, 13A30
Published electronically:
June 9, 2006
MathSciNet review:
2240653
Fulltext PDF Free Access
Abstract 
References 
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Abstract: Let be a multiplicative filtration of a local ring such that the Rees algebra is Noetherian. We recall Burch's inequality for and give an upper bound of the ainvariant of the associated graded ring using a reduction system of . Applying those results, we study the symbolic Rees algebra of certain ideals of dimension .
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Valabrega, P. and Valla, G., Form rings and regular sequences, Nagoya Math. J., 72 (1978), 93101. MR 0514892 (80d:14010)
 1.
 Aberbach, I., Huneke, C. and Trung, N. V., Reduction numbers, BriançonSkoda theorem and the depth of Rees rings, Compositio Math., 97 (1995), 403434. MR 1353282 (96g:13002)
 2.
 Bruns, W. and Vetter, U., Determinantal rings, Lecture Notes in Math., 1327, Springer, 1988. MR 0953963 (89i:13001)
 3.
 Burch, L., Codimension and analytic spread, Proc. Camb. Philos. Soc., 72 (1972), 369373.MR 0304377 (46:3512)
 4.
 Conca, A., Straightening law and powers of determinantal ideals of Hankel matrices, Adv. Math., 138 (1998), 263292.MR 1645574 (99i:13020)
 5.
 Goto, S. and Nishida, K., The CohenMacaulay and Gorenstein Rees algebras associated to filtrations, Mem. Amer. Math. Soc., 526 (1994).MR 1287443 (95b:13001)
 6.
 Goto, S., Nishida, K. and Shimoda, Y., Topics on symbolic Rees algebras for space monomial curves, Nagoya Math. J., 124 (1991), 99132. MR 1142978 (93e:13002)
 7.
 Goto, S. and Watanabe, K., On graded rings I, J. Math. Soc. Japan, 30 (1978), 179213. MR 0494707 (81m:13021)
 8.
 Johnston, B. and Katz, D., Castelnuovo regularity and graded rings associated to an ideal, Proc. Amer. Math. Soc., 123 (1995), 727734. MR 1231300 (95d:13005)
 9.
 Nishida, K., On filtrations having small analytic deviation, Comm. Algebra, 29 (2001), 27112729. MR 1845138 (2002k:13006)
 10.
 Nishida, K., On the depth of the associated graded ring of a filtration, J. Algebra, 285 (2005), 182195. MR 2119110
 11.
 Peskine, C. and Szpiro, L., Liaison des variétés algébriques I, Invent. Math. 26 (1974), 271302. MR 0364271 (51:526)
 12.
 Valabrega, P. and Valla, G., Form rings and regular sequences, Nagoya Math. J., 72 (1978), 93101. MR 0514892 (80d:14010)
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Additional Information
Y. Kinoshita
Affiliation:
Division of Mathematical Sciences and Physics, School of Science and Technology, Chiba University, 2638522, Japan
K. Nishida
Affiliation:
Division of Mathematical Sciences and Physics, School of Science and Technology, Chiba University, 2638522, Japan
Email:
nishida@math.s.chibau.ac.jp
Y. Yamanaka
Affiliation:
Division of Mathematical Sciences and Physics, School of Science and Technology, Chiba University, 2638522, Japan
A. Yoneda
Affiliation:
Division of Mathematical Sciences and Physics, School of Science and Technology, Chiba University, 2638522, Japan
DOI:
http://dx.doi.org/10.1090/S0002993906084292
PII:
S 00029939(06)084292
Keywords:
Multiplicative filtration,
Rees algebra,
associated graded ring
Received by editor(s):
April 22, 2004
Received by editor(s) in revised form:
July 1, 2005
Published electronically:
June 9, 2006
Additional Notes:
The second author was supported by the GrantinAid for Scientific Researches in Japan (C) (2) No. 15540009
Communicated by:
Bernd Ulrich
Article copyright:
© Copyright 2006 American Mathematical Society
