Maximal Cohen--Macaulay modules over hypersurface rings.
Meandering of trajectories of polynomial vector fields in the affine n-space.
We give an explicit upper bound for the number of isolated intersections between an integral curve of a polynomial vector field in Rn and an affine hyperplane.The problem turns out to be closely related to finding an explicit upper bound for the length of ascending chains of polynomial ideals spanned by consecutive derivatives.This exposition constitutes an extended abstract of a forthcoming paper: only the basic steps are outlined here, with all technical details being either completely omitted...
Minimal resolutions of lattice ideals and integer linear programming.
A combinatorial description of the minimal free resolution of a lattice ideal allows us to the connection of Integer Linear Programming and Al1gebra. The non null reduced homology spaces of some simplicial complexes are the key. The extremal rays of the associated cone reduce the number of variables.
More on polynomial Bézoutians with respect to a general basis.