9 citations · 12 across the 7 of their papers we have counts for
11 papers
DG Algebra Structures on Mapping Cones with an Application to Edge Ideals
Hugh Geller, Desiree Martin, Matthew Mastroeni +1
We generalize a construction of Herzog and Takayama pertaining to differential graded algebra structures on mapping cones. Via this generalization, we provide the minimal free reso…
Koszul Graded Möbius Algebras and Strongly Chordal Graphs
Adam LaClair, Matthew Mastroeni, Jason McCullough +1
The graded Möbius algebra of a matroid is a commutative graded algebra which encodes the combinatorics of the lattice of flats of the matroid. As a special subalgebra of the augmen…
Depth and Singular Varieties of Exterior Edge Ideals
Matthew Mastroeni, Jason McCullough, Andrew Osborne +2
Edge ideals of finite simple graphs are well-studied over polynomial rings. In this paper, we initiate the study of edge ideals over exterior algebras, specifically focusing on the…
Chow rings of matroids are Koszul
Matthew Mastroeni, Jason McCullough
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 by Brad…
The structure of Koszul algebras defined by four quadrics
Paolo Mantero, Matthew Mastroeni
Avramov, Conca, and Iyengar ask whether for all when is a Koszul algebra minimally defined by quadrics. In recent work, we give an affi…
The InvariantRing package for Macaulay2
Luigi Ferraro, Federico Galetto, Francesca Gandini +3
We describe a significant update to the existing InvariantRing package for Macaulay2. In addition to expanding and improving the methods of the existing package for actions of fini…
Computing generalized Frobenius powers of monomial ideals
Christopher A. Francisco, Matthew Mastroeni, Jeffrey Mermin +1
Generalized Frobenius powers of an ideal were introduced in work of Hernández, Teixeira, and Witt as characteristic-dependent analogs of test ideals. However, little is known about…
Betti numbers of Koszul algebras defined by four quadrics
Paolo Mantero, Matthew Mastroeni
Let be an ideal generated by quadrics in a standard graded polynomial ring over a field. A question of Avramov, Conca, and Iyengar asks whether the Betti numbers of $R = S/…
Quadratic Gorenstein rings and the Koszul property II
Matthew Mastroeni, Hal Schenck, Mike Stillman
A question of Conca, Rossi, and Valla asks whether every quadratic Gorenstein ring of regularity three is Koszul. In a previous paper, we use idealization to answer their quest…
Quadratic Gorenstein rings and the Koszul property I
Matthew Mastroeni, Hal Schenck, Mike Stillman
Let be a standard graded Gorenstein algebra over a field presented by quadrics. Conca, Rossi, and Valla have shown that such a ring is Koszul if or if…
Koszul almost complete intersections
Matthew Mastroeni
Let be a quotient of a standard graded polynomial ring by an ideal generated by quadrics. If is Koszul, a question of Avramov, Conca, and Iyengar asks whether…