Fuxiang Yang

University of Notre Dame

Syzygies of virtually linear ideals

We study the homological properties of ideals with partially linear (virtual) resolutions in a polynomial ring. We establish an effective bound beyond which their powers coincide with a power of the maximal ideal, proving a slightly weaker version of the Eisenbud-Huneke-Ulrich conjecture for a more general class of ideals. We also obtain an upper bound on their Castelnuovo-Mumford regularity, extending Macaulay’s bound and a theorem of Eisenbud-Huneke-Ulrich.