Behavior of local cohomology modules under polarization
نویسنده
چکیده
Let S = k[x1, . . . , xn] be a polynomial ring over a field k with n variables x1, . . . , xn, m the irrelevant maximal ideal of S, I a monomial ideal in S and I ′ the polarization of I in the polynomial ring S′ with ρ variables. We show that each graded piece H i m (S/I)a, a ∈ Z , of the local cohomology module H i m (S/I) is isomorphic to a specific graded pieceH i+ρ−n m ′ (S′/I )α, α ∈ Z , of the local cohomology module H i+ρ−n m ′ (S′/I ′), where m′ is the irrelevant maximal ideal of S′.
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