2025/05/23 by Puthenpurakal, Tony J., Reddy, Rakesh B. T.
#Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13D45 #Secondary 13N10
paper · doi:10.48550/arxiv.2505.17597
Let K be a field of characteristic zero. Let R = K[X0, X1,…,Xn] be standard graded. Let An+1(K) be the (n + 1)th Weyl algebra over K. Let I be a homogeneous ideal of R and let M = HiI(R) for some i ≥ 0. By a result of Lyubeznik, M is a graded holonomic An +1(K)-module for each i ≥ 0. Let χc(∂, M) (χc(X, M)) be the Euler characteristics of de Rham cohomology (resp. Koszul cohomology) of M. We prove χc(∂, M) = (-1)n+1χc(X, M).