Chow rings of matroids are Koszul
M Mastroeni, J McCullough - Mathematische Annalen, 2023 - Springer
Chow rings of matroids were instrumental in the resolution of the Heron–Rota–Welsh
Conjecture by Adiprasito, Huh, and Katz and in the resolution of the Top-Heavy Conjecture …
Conjecture by Adiprasito, Huh, and Katz and in the resolution of the Top-Heavy Conjecture …
On the Lefschetz property for quotients by monomial ideals containing squares of variables
Let Δ be an (abstract) simplicial complex on n vertices. One can define the Artinian
monomial algebra A (Δ)= k [x 1,…, xn]/〈 x 1 2,…, xn 2, I Δ〉, where k is a field of characteristic …
monomial algebra A (Δ)= k [x 1,…, xn]/〈 x 1 2,…, xn 2, I Δ〉, where k is a field of characteristic …
Artinian algebras and Jordan type
A Iarrobino, P Macias Marques, C McDaniel - 2022 - projecteuclid.org
There has been much work on strong and weak Lefschetz conditions for graded Artinian
algebras A, especially those that are Artinian Gorenstein. A more general invariant of an …
algebras A, especially those that are Artinian Gorenstein. A more general invariant of an …
Artinian algebras and Jordan type
A Iarrobino, PM Marques, C McDaniel - arXiv preprint arXiv:1802.07383, 2018 - arxiv.org
The Jordan type of an element $\ell $ of the maximal ideal of an Artinian k-algebra A acting
on an A-module M of k-dimension n, is the partition of n given by the Jordan block …
on an A-module M of k-dimension n, is the partition of n given by the Jordan block …
On the socle of Artinian algebras associated with graphs
J Neves - Journal of Algebraic Combinatorics, 2023 - Springer
Given a simple graph, consider the polynomial ring with coefficients in a field and variables
identified with the edges of the graph. Given a non-empty even cardinality Eulerian …
identified with the edges of the graph. Given a non-empty even cardinality Eulerian …
Quadratic Gorenstein rings and the Koszul property I
M Mastroeni, H Schenck, M Stillman - Transactions of the American …, 2021 - ams.org
Let $ R $ be a standard graded Gorenstein algebra over a field presented by quadrics. In
[Compositio Math. 129 (2001), no. 1, 95–121], Conca-Rossi-Valla show that such a ring is …
[Compositio Math. 129 (2001), no. 1, 95–121], Conca-Rossi-Valla show that such a ring is …
Koszul Gorenstein Algebras From Cohen–Macaulay Simplicial Complexes
A D'Alì, L Venturello - International Mathematics Research …, 2023 - academic.oup.com
We associate with every pure flag simplicial complex a standard graded Gorenstein-algebra
whose homological features are largely dictated by the combinatorics and topology of. As …
whose homological features are largely dictated by the combinatorics and topology of. As …
Quadratic Gorenstein rings and the Koszul property II
M Mastroeni, H Schenck… - International Mathematics …, 2023 - academic.oup.com
Abstract Conca–Rossi–Valla ask if every quadratic Gorenstein ring of regularity three is
Koszul. In, we use idealization to answer their question, proving that in nine or more …
Koszul. In, we use idealization to answer their question, proving that in nine or more …
Subadditivity, strand connectivity and multigraded Betti numbers of monomial ideals
AV Jayanthan, A Kumar - Journal of Commutative Algebra, 2023 - projecteuclid.org
Let R= 𝕂 [x 1,…, xn] and I⊂ R be a homogeneous ideal. We first obtain certain sufficient
conditions for the subadditivity condition of R/I. As a consequence, we prove that if I is …
conditions for the subadditivity condition of R/I. As a consequence, we prove that if I is …
On the rate of generic Gorenstein -algebras
M Boij, E De Negri, A De Stefani, ME Rossi - arXiv preprint arXiv …, 2023 - arxiv.org
The rate of a standard graded $ K $-algebra $ A $ is a measure of the growth of the shifts in
a minimal free resolution of $ K $ as an $ A $-module. In particular $ A $ has rate one if and …
a minimal free resolution of $ K $ as an $ A $-module. In particular $ A $ has rate one if and …