  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.
