17 research outputs found
Regularity of squarefree monomial ideals
We survey a number of recent studies of the Castelnuovo-Mumford regularity of
squarefree monomial ideals. Our focus is on bounds and exact values for the
regularity in terms of combinatorial data from associated simplicial complexes
and/or hypergraphs.Comment: 23 pages; survey paper; minor changes in V.
Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension
Let be a local ring, and let and be finitely generated
-modules such that has finite complete intersection dimension. In this
paper we define and study, under certain conditions, a pairing using the
modules \Ext_R^i(M,N) which generalizes Buchweitz's notion of the Herbrand
diference. We exploit this pairing to examine the number of consecutive
vanishing of \Ext_R^i(M,N) needed to ensure that \Ext_R^i(M,N)=0 for all
. Our results recover and improve on most of the known bounds in the
literature, especially when has dimension at most two
Techniques for the study of singularities with applications to resolution of 2-dimensional schemes
We give an overview of invariants of algebraic singularities over perfect
fields. We then show how they lead to a synthetic proof of embedded resolution
of singularities of 2-dimensional schemes.Comment: 26 pages; minor changes have been adde
Polarized endomorphisms of complex normal varieties
10.1007/s00208-009-0420-yMathematische Annalen3464991-101