Ideals with larger projective dimension and regularity

Bounds for the Regularity of Edge Ideal of Vertex Decomposable and Shellable Graphs

Bounds on the Regularity and Projective Dimension of Ideals Associated to Graphs

In this paper we give new upper bounds on the regularity of edge ideals whose resolutions are k-steps linear; surprisingly, the bounds are logarithmic in the number of variables. We also give various bounds for the projective dimension of such ideals, generalizing other recent results. By Alexander duality, our results also apply to unmixed square-free monomial ideals of codimension two. We als...

Regularity, Depth and Arithmetic Rank of Bipartite Edge Ideals

We study minimal free resolutions of edge ideals of bipartite graphs. We associate a directed graph to a bipartite graph whose edge ideal is unmixed, and give expressions for the regularity and the depth of the edge ideal in terms of invariants of the directed graph. For some classes of unmixed edge ideals, we show that the arithmetic rank of the ideal equals projective dimension of its quotient.

Irena Peeva

S OF SOME OF MY PAPERS GROUPED BY TOPIC 1. Regularity. Let k be an algebraically closed field. We will work over a standard graded polynomial ring U over k. Projective dimension and regularity are the main numerical invariants that measure the complexity of a minimal free resolution. Let L be a homogeneous ideal in U , and let b ij (L) be its graded Betti numbers. The projective dimension pd(L)...

Generic Projection Methods and Castelnuovo Regularity of Projective Varieties

For a reduced, irreducible projective variety X of degree d and codimension e in P the Castelnuovo-Mumford regularity regX is defined as the least k such that X is k-regular, i.e. H(P , IX(k− i)) = 0 for i ≥ 1, where IX ⊂ OPN is the sheaf of ideals of X. There is a long standing conjecture about k-regularity (see [EG]): regX ≤ d−e+1. Generic projection methods proved to be effective for the stu...