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Hilbert polynomials of multigraded filtrations of ideals

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Title Hilbert polynomials of multigraded filtrations of ideals
 
Creator MASUTI, SK
SARKAR, P
VERMA, JK
 
Subject REES-ALGEBRAS
COHEN-MACAULAY
LOCAL COHOMOLOGY
COEFFICIENTS
REDUCTIONS
RINGS
MULTIPLICITIES
Hilbert polynomial
Analytically unramified local ring
Joint reductions
Local cohomology of Rees algebra
Joint reduction number
 
Description Hilbert functions and Hilbert polynomials of Z(s)-graded admissible filtrations of ideals {F((n) under bar)}((n) under bar is an element of zs) such that lambda (R/F((n) under bar)) is finite for all (n) under bar is an element of Z(s) are studied. Conditions are provided for the Hilbert function H-F((n) under bar) := lambda(R/F((n) under bar)) and the corresponding Hilbert polynomial P-F((n) under bar) to be equal for all (n) under bar is an element of N-s. A formula for the difference H-F-((n) under bar) - P-F((n) under bar) in terms of local cohomology of the extended Rees algebra of F is proved which is used to obtain sufficient linear relations analogous to the ones given by Huneke and Ooishi among coefficients of P-F((n) under bar) so that H-F((n) under bar) = P-F((n) under bar) for all (n) under bar is an element of N-s. A theorem of Rees about joint reductions of the filtration {I-r J(s)}(r,s is an element of z) is generalised for admissible filtrations of ideals in two-dimensional Cohen-Macaulay local rings. Necessary and sufficient conditions are provided for the multi-Rees algebra of an admissible Z(2)-graded filtration F to be Cohen-Macaulay. (C) 2015 Elsevier Inc. All rights reserved.
 
Publisher ACADEMIC PRESS INC ELSEVIER SCIENCE
 
Date 2016-01-14T14:11:39Z
2016-01-14T14:11:39Z
2015
 
Type Article
 
Identifier JOURNAL OF ALGEBRA, 444,527-566
0021-8693
1090-266X
http://dx.doi.org/10.1016/j.jalgebra.2015.07.032
http://dspace.library.iitb.ac.in/jspui/handle/100/17695
 
Language en