Combinatorial Koszul Homology: computations and Applications

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 algorithm...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autor principal: Sáenz de Cabezón Irigaray, Eduardo
Otros Autores: Hernández Paricio, Luis Javier (Universidad de La Rioja)
Formato: text (thesis)
Lenguaje:eng
Publicado: Universidad de La Rioja (España) 2008
Materias:
Acceso en línea:https://dialnet.unirioja.es/servlet/oaites?codigo=13745
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
Descripción
Sumario: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.