On minimal graded free resolutions

摘要: Minimal graded free resolutions are an important and central topic in algebra. They a useful tool for studying modules over finitely generated K- algebras. Such resolution determines the Hilbert series, Castelnuovo-Mumford regularity other invariants of module. This thesis is concerned with structure minimal resolutions. We relate our results to several recent trends commutative algebra. The first these deals relations between properties Stanley- Reisner ring associated simplicial complex Stanley-Reisner its Alexander dual. Another development investigation linear part graded free as defined by Eisenbud Schreyer. Several authors were interested problem give lower bounds Betti numbers module. In particular, Eisenbud-Koh, Green, Herzog Reiner- Welker studied Betti numbers which determine strand a minimal resolution. Bigraded algebras occur naturally many research areas algebra. A typical example bigraded algebra Rees ideal. Herzog and Trung used this study Castelnuovo- Mumford regularity powers ideals polynomial ring. Conca, Herzog, Trung Valla dealt diagonal subalgebras algebras. Aramova, Crona De Negri homological K-algebras.