Deterministic Determination of Axial Constants, Sectional Regularities and Annihilator Numbers

Abstract

Axial constants and sectional regularities are recently introduced invariants of homogeneous polynomial ideals that, like the already earlier introduced annihilator numbers, depend on generic choices of coordinates. We provide effective characterisations of the genericity underlying these invariants in terms of $β$-maximal position and strong stability. In particular, we show that $β$-maximal position suffices for determining generic annihilator numbers and sectional regularities, while its combination with strong stability yields corresponding results for axial constants. We also develop deterministic linear algebra procedures for detecting the required generic positions and for computing these invariants.