Combinatorial Koszul Homologycomputations and Applications stars

  1. Sáenz de Cabezón Irigaray, Eduardo
Supervised by:
  1. Luis Javier Hernández Paricio Director
  2. Werner M. Seiler Director

Defence university: Universidad de La Rioja

Fecha de defensa: 27 February 2008

Committee:
  1. Henry P. Wynn Chair
  2. Julio Rubio García Secretary
  3. María Isabel Bermejo Díaz Committee member
  4. Anna M. Bigatti Committee member
  5. Graham Ellis Committee member
Doctoral thesis with
  1. Mención internacional
Department:
  1. Matemáticas y Computación

Type: Thesis

Teseo: 171502 DIALNET lock_openDialnet editor
Institutional repository: lock_openOpen access Editor

Abstract

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.