Local cohomology of bigraded modules [Elektronische Ressource] / vorgelegt von Ahad Rahimi

Local cohomology of bigraded modulesDem Fachbereich 6Mathematik und Informatikder Universit¨at Duisburg-Essenzur Erlangung desDoktorgrades(Dr. rer. nat.)vorgelegt vonAhad Rahimiaus dem IranOctober 2007Vorsitzender: Prof. Dr. Wolfgang M. RuessErster Gutachter: Prof. Dr. Ju¨rgen HerzogZweiter Gutachter: Prof. Dr. Marc ChardinDedicated to my parents, my wife and my son AliAcknowledgmentsI am very grateful to my advisor Professor Ju¨rgen Herzog for his guidance, con-stant encouragement and support throughout the preparation of this thesis.I also express my gratitude to the university of Essen for its hospitality and thefacilities provided during my Ph.D study and research.Finally, I would like to thank the ministry of Science, Research and Technologyof Islamic Republic of Iran for the financial support offered me during my study.ContentsPreface 11 Preliminaries 41.1 Graded rings and graded modules . . . . . . . . . . . . . . . . . . . . 41.2 Local cohomology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Castelnuovo-Mumford regularity and Hilbert function . . . . . . . . 91.4 Stanley-Reisner rings . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.5 Spectral sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.6 Tameness and local cohomology . . . . . . . . . . . . . . . . . . . . . 161.7 Graded and bigraded local cohomology . . . . . . . . . . . . . . . . .