Aeppli-Bott-Chern-Massey Products, Bigraded Notions of Formality, and Non-Zero Degree Maps

Abstract

We introduce and study notions of bigraded formality for the algebra of forms on a complex manifold, along with their relation to higher Aeppli-Bott-Chern-Massey products which extend, in an augmented setting, the case of triple products studied by Angella-Tomassini. We show that these Aeppli-Bott-Chern-Massey products on complex manifolds pull back non-trivially to the blow-up along a complex submanifold, as long their degree is less than the real codimension of the submanifold. We then consider the general question of under which conditions formality is preserved by non-zero degree maps.