The main goal of the paper is to generalize Castelnuovo-Mumford regularity for coherent sheaves on projective spaces to coherent sheaves on n-dimensional smooth projective varieties X with an n-block collection B which generates the bounded derived category Db(OX -mod). To this end, we use the theory of n-blocks and Beilinson type spectral sequence to define the notion of regularity of a cohere...

KOSZUL ALGEBRAS, CASTELNUOVO-MUMFORD REGULARITY, AND GENERIC INITIAL IDEALS Giulio Caviglia The University of Kansas Advisor: Craig Huneke August, 2004 The central topics of this dissertation are: Koszul Algebras, bounds for the Castelnuovo Mumford regularity, and methods involving the use of generic changes of coordinates and generic hyperplane restrictions. We give an introduction to Koszul a...

This paper characterizes the Castelnuovo-Mumford regularity by evaluating the initial ideal with respect to the reverse lexicographic order.

This paper characterizes the Castelnuovo-Mumford regularity by evaluating the initial ideal with respect to the reverse lexicographic order.

This paper gives explicit formulas for the reduction number and Castelnuovo–Mumford regularity of projective monomial curves.

Bounds for the Castelnuovo-Mumford regularity and Hilbert coefficients are given in terms of the arithmetic degree (if the ring is reduced) or in terms of the defining degrees. From this it follows that there exists only a finite number of Hilbert functions associated with reduced algebras over an algebraically closed field with a given arithmetic degree and dimension. A good bound is also give...

The paper begins by overviewing the basic facts on geometric exceptional collections. Then, we derive, for any coherent sheaf F on a smooth projective variety with a geometric collection, two spectral sequences: the first one abuts to F and the second one to its cohomology. The main goal of the paper is to generalize Castelnuovo-Mumford regularity for coherent sheaves on projective spaces to co...