  Quasi-stable ideals appear as leading ideals in the theory of Pommaret bases.
We show that quasi-stable leading ideals share many of the properties of the
generic initial ideal. In contrast to genericity, quasi-stability is a
characteristic independent property that can be effectively verified. We also
relate Pommaret bases to some invariants associated with local cohomology,
exhibit the existence of linear quotients in Pommaret bases and prove some
results on componentwise linear ideals.
