5 papers · 1 filter
Powers of monomial ideals with characteristic-dependent Betti numbers
Davide Bolognini, Antonio Macchia, Francesco Strazzanti +1
We explore the dependence of the Betti numbers of monomial ideals on the characteristic of the field. A first observation is that for a fixed prime either the -th Betti numb…
The minimal cellular resolutions of the edge ideals of forests
Margherita Barile, Antonio Macchia
We present an explicit construction of a minimal cellular resolution for the edge ideals of forests, based on discrete Morse theory. In particular, the generators of the free modul…
On determinantal ideals and algebraic dependence
Margherita Barile, Antonio Macchia
Let be a matrix with entries in a polynomial ring over an algebraically closed field . We prove that, if the entries of outside some -submatrix are algebra…
Binomial edge ideals of bipartite graphs
Davide Bolognini, Antonio Macchia, Francesco Strazzanti
We classify the bipartite graphs whose binomial edge ideal is Cohen-Macaulay. The connected components of such graphs can be obtained by gluing a finite number of basic b…
Regularity of the vanishing ideal over a parallel composition of paths
Antonio Macchia, Jorge Neves, Maria Vaz Pinto +1
Let G be a graph obtained by taking r>=2 paths and identifying all first vertices and identifying all the last vertices. We compute the Castelnuovo--Mumford regularity of the quoti…