Computing local cohomology of the fiber cone in Macaulay2

[Anoot Yadav]

Hi,

I am trying to compute the local cohomology modules of the fiber cone of an ideal using Macaulay2, but so far I have not been successful.

More precisely, let (A , m) be a Noetherian local (or standard graded) ring and I⊆A an m-primary ideal. The fiber cone is

F(I)=⨁_{n\geq 0}​I^n/m*I^n.

I am using the HH^1(F(I)) command, but it does not work.

My questions are:

1. Is there a recommended way in Macaulay2 to construct the fiber cone F(I) so that its local cohomology can be computed?

2. Is there any existing code, package, or workaround (e.g. using Rees algebras, multigradings, or Čech complexes) that allows the computation of local cohomology modules of the fiber cone?

3. Are there known limitations in Macaulay2 regarding local cohomology of non-standard graded algebras such as fiber cones?

Any guidance, references, or sample code would be greatly appreciated.

Thank you very much for your time and help.

Thanks

Anoot