Michael Gintz | Searcharxiv

arXiv2026

Cohomological support varieties of certain monomial ideals

Building on work of Briggs, Grifo and Pollitz arXiv:2506.10827, we give an example of two cohomological support varieties of monomial ideals which are not unions of linear subspaces. We provide a procedure for the computation of the cohomological support varieties of certain other monomial ideals - including those with homogeneous generators - with improved computational efficiency, leading to a computer-assisted verification of the existence of a third support variety of a monomial ideal which is not a union of linear subspaces and a computer-assisted proof of a classification of cohomological support varieties of homogeneous monomial ideals over $\mathbb{Q}$ with 6 generators.

math.AC↗

arXiv2025

Koszul cohomology and support of local cohomology modules of complete intersections

Let $R$ be a noetherian commutative ring and $f_1,\dots,f_c$ be a regular sequence in $R$. We introduce a framework to study $Supp(H^j_I(R/(f_1,\dots,f_c)))$ by linking the Koszul cohomology of $H^j_I(R)$ on the sequence $f_1,\dots,f_c$ and local cohomology modules $H^j_I(R/(f_1,\dots,f_c))$. As an application, we prove that if $R$ is a noetherian regular ring of prime characteristic $p$ and $f_1,f_2$ form a regular sequence in $R$ then $Supp(H^j_I(R/(f_1,f_2)))$ is Zariski-closed for each integer $j$ and each ideal $I$.

math.AC↗