18 citations · 66 across the 29 of their papers we have counts for
20 papers · 1 filter
-graded rings and their canonical modules
Margherita Barile, Winfried Bruns
In ``Cohen--Macaulay rings'' Bruns and Herzog define the graded canonical module for -graded rings. We generalize the definition to multigradings and prove that the c…
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…
The arithmetical rank of the edge ideals of cactus graphs
Margherita Barile, Antonio Macchia
We prove that, for the edge ideal of a cactus graph, the arithmetical rank is bounded above by the sum of the number of cycles and the maximum height of its associated primes. The…
The arithmetical rank of the edge ideals of graphs with pairwise disjoint cycles
Margherita Barile, Antonio Macchia
We prove that, for the edge ideal of a graph whose cycles are pairwise vertex-disjoint, the arithmetical rank is bounded above by the sum of the number of cycles and the maximum he…
Projective dimensions of the edge ideals of forests
Margherita Barile
This paper is currently undergoing revision.