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We introduce a notion of sectional regularity for a homogeneous ideal 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. 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.more » « less
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Abstract We introduce the cohomological blowup of a graded Artinian Gorenstein algebra along a surjective map, which we term BUG (blowup Gorenstein) for short. This is intended to translate to an algebraic context the cohomology ring of a blowup of a projective manifold along a projective submanifold. We show, among other things, that a BUG is a connected sum, that it is the general fiber in a flat family of algebras, and that it preserves the strong Lefschetz property. We also show that standard graded compressed algebras are rarely BUGs, and we classify those BUGs that are complete intersections. We have included many examples throughout this manuscript.more » « less
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Miller, Claudia ; Striuli, Janet ; Witt, Emily (Ed.)
