Cohomological Blow Ups of Graded Artinian Gorenstein Algebras Along Surjective Maps

Authors

Anthony Iarrobino, Northeastern University
Pedro Macias Marques, Universidade de Évora
Chris McDaniel, Endicott College
Alexandra Seceleanu, University of Nebraska-LincolnFollow
Junzo Watanabe, Tokai University

Date of this Version

9-10-2021

Citation

Published (2023) International Mathematics Research Notices, 2023 (7), pp. 5816-5886.

Comments

Used by permission.

Abstract

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 complete intersections. We have included many examples throughout this manuscript.