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...

Let I be a homogeneous ideal of the polynomial ring K[x0, . . . , xn], where K is an arbitrary field. Avoiding the construction of a minimal graded free resolution of I, we provide effective methods for computing the Castelnuovo-Mumford regularity of I that also compute other cohomological invariants of K[x0, . . . , xn]/I. We then apply our methods to the defining ideal I(V) of a projective mo...

The Castelnuovo-Mumford regularity of a module gives a rough measure of its complexity. We bound the regularity of a module given an approximation by modules whose regularities are known. Such approximations can arise naturally for modules constructed by inductive combinatorial means. We apply these methods to bound the regularity of ideals constructed as combinations of linear ideals and the m...

We study the initial ideal of binomial edge ideal in degree 2 ([in<(JG)]2), associated to a graph G. We computed dimension, depth, Castelnuovo-Mumford regularity, Hilbert function and Betti numbers of [in<(JG)]2 for some classes of graphs. AMS Mathematics Subject Classification (2010): 05E40, 16E30