  A notion of sectional regularity for a homogeneous ideal $I$, which measures
the regularity of its generic sections with respect to linear spaces of various
dimensions, is introduced. 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 $I$. The equivalence of these
notions and several other homological and ideal-theoretic invariants is shown.
It is also established that these equivalent invariants grow linearly for the
family of powers of a given ideal.
