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Title: Cohomological Blowups of Graded Artinian Gorenstein Algebras along Surjective Maps
Authors: Iarrobino, Anthony
Macias Marques, Pedro
McDaniel, Chris
Seceleanu, Alexandra
Watanabe, Junzo
Keywords: Artinian Gorenstein
cohomology ring
blow up
cohomological blow-up algebra
connected sum
flat family
complete intersection
Hilbert function
Lefschetz property
Macaulay dual generator
Issue Date: 2023
Publisher: International Mathematics Research Notices
Citation: Anthony Iarrobino, Pedro Macias Marques, Chris McDaniel, Alexandra Seceleanu, and Junzo Watanabe (2023), Cohomological Blowups of Graded Artinian Gorenstein Algebras along Surjective Maps, International Mathematics Research Notices, vol. 2023, n.º 7, pp. 5816–5886
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.
Type: article
Appears in Collections:MAT - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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