Axial constants and sectional regularity of homogeneous ideals

Abstract

We introduce a notion of sectional regularity for a homogeneous ideal I I , which measures the regularity of its general sections with respect to linear spaces of various dimensions. It is related to axial constants defined as the intercepts on the coordinate axes of the set of exponents of monomials in the reverse lexicographic generic initial ideal of I I . We show the equivalence of these notions and several other homological and ideal-theoretic invariants. We also establish that these equivalent invariants grow linearly for the family of powers of a given ideal.