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20212026
most citedMixed Hodge structure on local cohomology with support in determinantal varieties

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math.AG2026

Calculating Hodge and weight filtrations on localizations

András C. Lőrincz, Michael Perlman

We describe the Macaulay2 package MixedHodgeModules, which computes Hodge and weight filtrations on localizations S_f of a polynomial ring S at a non-constant reduced polynomial f,…

math.AG2026

Local cohomology with Schubert support on compact Hermitian symmetric spaces

Michael Perlman

We consider local cohomology sheaves on compact Hermitian symmetric spaces supported in Schubert varieties, which carry natural structures as mixed Hodge modules. Our main result g…

math.AG2026

Microlocal Bernstein--Sato polynomials on singular ambient varieties

Bradley Dirks, Michael Perlman

We introduce the microlocal Bernstein--Sato polynomial of a function on a possibly singular ambient variety, extending the theory of Saito. We show that, contrary to the smooth amb…