The grade of the leading-form ideal in the form ring equals the least index at which the Khadam-Schenzel local cohomology variant L^i does not vanish.
Grothendieck: ‘Local cohomology’, Notes by R
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A criterion of Cohen Macaulayness of the form module
The grade of the leading-form ideal in the form ring equals the least index at which the Khadam-Schenzel local cohomology variant L^i does not vanish.