Let I be a homogeneous ideal of S = K[x1,..., xn] and let J be an initial ideal of I with respect to a term order. We prove that if J is radical then the Hilbert functions of the local cohomology modules supported at the homogeneous maximal ideal of S/I and S/J coincide. In particular,depth(S/I) = depth(S/J ) and reg(S/I) = reg(S/J
Square-free Gröbner degenerations
A. Conca;M. Varbaro
2020-01-01
Abstract
Let I be a homogeneous ideal of S = K[x1,..., xn] and let J be an initial ideal of I with respect to a term order. We prove that if J is radical then the Hilbert functions of the local cohomology modules supported at the homogeneous maximal ideal of S/I and S/J coincide. In particular,depth(S/I) = depth(S/J ) and reg(S/I) = reg(S/J
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