Homología de Koszul Combinatoria: Cálculo y Aplicaciones(Combinatorial Koszul Homology, Computations and Applications)

Autor: Sáenz de Cabezón Irigaray, Eduardo

Tipo de documento: Tesis

Director/es: Hernández Paricio, Luis Javier

Universidad: Universidad de La Rioja

Año: 2008 

Texto completo open access 

Resumen: With a particular focus on explicit computations and applications of the Koszul homology and Betti numbers of monomial ideals, the main goals od 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.