The combinatorial calculation of algebraic invariants of a monomial ideal
Commutative Algebra
2017-08-25 v1
Abstract
We introduce the combinatorial Lyubeznik resolution of monomial ideals. We prove that this resolution is isomorphic to the usual Lyubezbnik resolution. As an application, we give a combinatorial method to determine if an ideal is a Lyubeznik ideal. Furthermore, the minimality of the Lyubeznik resolution is characterized and we classify all the Lyubeznik symbols using combinatorial criteria. We get a combinatorial expression for the projective dimension, the length of Lyubeznik, and the arithmetical rank of a monomial ideal. We define the Lyubeznik totally ideals as those ideals that yield a minimal free resolution under any total order. Finally, we present that for a family of graphics, that their edge ideals are Lyubeznik totally ideals.
Keywords
Cite
@article{arxiv.1708.07255,
title = {The combinatorial calculation of algebraic invariants of a monomial ideal},
author = {Luis A. Dupont and Daniel G. Mendoza and Miriam Rodríguez},
journal= {arXiv preprint arXiv:1708.07255},
year = {2017}
}