Deformations of finite dimensional algebras and their idempotents

Let B be a finite dimensional algebra over an algebraically closed field K. If we represent primitive idempotents by points and basis vectors in eiBej by “arrows” from ej to ez, then any specialization of the algebra acts on this directed graph by coalescing points. This implies that the number of irreducible components in the scheme parametrizing n-dimensional algebras is no less than the number of loopless directed graphs with a total of n vertices and arrows. We also show that the condition of having a distributive ideal lattice is open.