On a Relation Between de Rham Cohomology of H (f) 1 (R) and the Koszul Cohomology of ∂(f) in R/(f)

Tony J. Puthenpurakal () and Rakesh B. T. Reddy ()
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Tony J. Puthenpurakal: IIT Bombay
Rakesh B. T. Reddy: IIT Bombay

Indian Journal of Pure and Applied Mathematics, 2018, vol. 49, issue 1, 71-86

Abstract: Abstract Let K be a field of characteristic zero, R = K[X1, ..., X n ]. Let A n (K) = K be the n th Weyl algebra over K. We consider the case when R and A n (K) is graded by giving deg X i = ω i and deg ∂ i = -ω i for i = 1, ..., n (here ω i are positive integers). Set ω = Σ k=1 n ω 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 compute the de Rham cohomology modules H j (∂;H (f) 1 (R)) for j ≤ n - 2 when V (f) is a smooth hypersurface in ℙ n (equivalently A = R/(f) is an isolated singularity).

Keywords: Local cohomology; associated primes; D-modules; Koszul homology (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s13226-018-0253-z

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