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Polynomial Growth Of Betti Sequences Over Local Rings, Luchezar L. Avramov, Alexandra Seceleanu, Zheng Yang
Polynomial Growth Of Betti Sequences Over Local Rings, Luchezar L. Avramov, Alexandra Seceleanu, Zheng Yang
Department of Mathematics: Faculty Publications
We study sequences of Betti numbers (βRi (M)) of finite modules M over a complete intersection local ring, R. It is known that for every M the subsequence with even, respectively, odd indices i is eventually given by some polynomial in i. We prove that these polynomials agree for all R-modules if the ideal I☐ generated by the quadratic relations of the associated graded ring of R satisfies height I☐ ≥ codim R − 1, and that the converse holds when R is homogeneous and when codim R ≤ 4. Avramov, …
Cohomological Blow Ups Of Graded Artinian Gorenstein Algebras Along Surjective Maps, Anthony Iarrobino, Pedro Macias Marques, Chris Mcdaniel, Alexandra Seceleanu, Junzo Watanabe
Cohomological Blow Ups Of Graded Artinian Gorenstein Algebras Along Surjective Maps, Anthony Iarrobino, Pedro Macias Marques, Chris Mcdaniel, Alexandra Seceleanu, Junzo Watanabe
Department of Mathematics: Faculty Publications
We introduce the cohomological blow up of a graded Artinian Gorenstein (AG) algebra along a surjective map, which we term BUG (Blow Up Gorenstein) for short. This is intended to translate to an algebraic context the cohomology ring of a blow up 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 …