Year: 2008
Type: preprint
Abstract: With a particular focus on explicit computations and applications of the Koszul homology and Betti numbers of monomial ideals, the main goals of this thesis are the following: Analyze the Koszul homology of monomial ideals and apply it to describe the structure of monomial ideals. Describe algorithms to perform efficient computations of the homological invariants of monomial ideals. Apply the theory and computations on monomial ideals to problems inside and outside mathematics The thesis introduces as a main tool Mayer-Vietoris trees of monomial ideals.
Source: arXiv (Cornell University)
Author: Saenz-de-Cabezon, Eduardo
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1483696128