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.

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.

In this article we fix a prime integer p and compare certain dg algebra resolutions over a local ring whose residue field has characteristic p. Namely, we show that given a closed surjective map between such algebras there is a precise description for the minimal model in terms of the acyclic closure, and that the latter is a quotient of the former. A first application is that the homotopy Lie algebra of a closed surjective map with residual characteristic p is abelian. We also use these calculations to show deviations enjoy rigidity properties which detect the (quasi-)complete intersection property.

In this article, we fix a prime integer p and compare certain dg algebra resolutions over a local ring whose residue field has characteristic p. Namely, we show that given a closed surjective map between such algebras there is a precise description for the minimal model in terms of the acyclic closure and that the latter is a quotient of the former. A first application is that the homotopy Lie algebra of a closed surjective map is abelian. We also use these calculations to show deviations enjoy rigidity properties which detect the (quasi-)complete intersection property.