Computing Koszul Homology for Monomial Ideals
Eduardo Saenz de Cabezon
Abstract
The Koszul homology of modules of the polynomial ring R is a central object in commutative algebra.It is strongly related with the minimal free resolution of these modules, and thus with regularity, Hilbert functions, etc. Here we consider the case of modules of the form R/I where I is a monomial ideal. So far, some good algorithms have been given in the literature and implemented in different Computer Algebra Systems (e.g. CoCoa, Singular, Macaulay), which compute minimal free resolutions of modules of the form R/I with I an ideal in R, which include the case of I being a monomial ideal as a particular one (a good review is given in Sie). Our goal is to build algorithms especially teargeted to monomial ideals, taking into account the special combinatorial and structural properties of these ideals. This being a first goal, it is also a first step of an alternative approach to the computation of the Koszul homology and minimal free resolutions of polynomial ideals.
Create a lesson
Related papers
On the weak Lefschetz property of Artinian Gorenstein algebras of codimension three in arbitrary characteristic
Omkar Javadekar
Linear Independence of Polynomial Compositions and Identifiability of Deep Neural Networks
Kathlén Kohn, Giovanni Luca Marchetti, Alex Massarenti et al.
Comparing v-numbers of symbolic and ordinary powers of squarefree monomial ideals
Trung Chau, Tài Huy Hà, A. V. Jayanthan et al.
Polynomial extensions do not preserve the strong finite type property
Viet-Hoang Tran, Phan Thanh Toan, Thieu N. Vo et al.
Reduction numbers for witnesses to the generalized Loewy length
Richard Bartels, Sarah Dajani, Gabriel Koomson
Multi-graded generic initial ideals, regularity, and the optimal colorful fractional Helly theorem for d-Leray complexes
Daniel McGinnis