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DE RHAM COHOMOLOGY OF LOCAL COHOMOLOGY MODULES: THE GRADED CASE

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Title DE RHAM COHOMOLOGY OF LOCAL COHOMOLOGY MODULES: THE GRADED CASE
 
Creator PUTHENPURAKAL, TJ
 
Description Let K be a field of characteristic zero, and let R= K[X-1, ... , X-n]. Let A(n) (K) = K < X-1, ... , X-n > be the nth Weyl algebra over K. We consider the case when R and A(n)(K) are graded by giving deg X-i = omega(i) and deg partial derivative(i) = -omega(i) for i = 1, ... ,n (here omega(i), are positive integers). Set omega = Sigma(n)(k=1) omega(k). Let I be a graded ideal in R. By a result due to Lyubeznik the local cohomology modules H-I(i)(R) are holonomic (A(n)(K))-modules for each i >= 0. In this article we prove that the de Rham cohomology modules H* (partial derivative; H-I* (R))(j) are concentrated in degree -omega; that is, H* (partial derivative; H-I* (R))(j) = 0 for j not equal -omega. As an application when A = R/(f) is an isolated singularity, we relate Hn-1(partial derivative; H-(f)(1) (R)) to Hn-1(partial derivative(f); A), the (n-1)th Koszul cohomology of A with respect to partial derivative(1)(f), ... , partial derivative(n)(f).
 
Publisher DUKE UNIV PRESS
 
Date 2016-01-15T10:09:45Z
2016-01-15T10:09:45Z
2015
 
Type Article
 
Identifier NAGOYA MATHEMATICAL JOURNAL, 217,1-21
0027-7630
2152-6842
http://dx.doi.org/10.1215/00277630-2857430
http://dspace.library.iitb.ac.in/jspui/handle/100/18334
 
Language en