Algebraic invariants of interval subdivided complexes

Abstract

We study ring-theoretic properties of the Stanley–Reisner rings of simplicial complexes that undergo the interval subdivisions. In particular, we establish results concerning computational description of dimension, Hilbert series, multiplicity, local cohomology, depth and regularity of the Stanley–Reisner ring of interval subdivided simplicial complex. We also prove results regarding the non-vanishing of graded Betti numbers and bounds on Betti numbers for these Stanley–Reisner rings.