Cohomological Blowups of Graded Artinian Gorenstein Algebras along Surjective Maps. (23rd February 2022)

• Record Type: Journal Article
• Authors: Iarrobino, Anthony; Macias Marques, Pedro; McDaniel, Chris; Seceleanu, Alexandra; Watanabe, Junzo
• Is Part Of: International mathematics research notices. Volume 2023:Number 7(2023)
• Page Start: 5816
• Page End: 5886
• Publication Date: 2022-02-23
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnac002
• Languages: English
• ISSNs: 1073-7928

Abstract

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.