Artinian Gorenstein algebras of embedding dimension four: components of PGor(H) for H=(1,4,7,…,1)

The proofs use properties of minimal resolutions, the smoothness of PGor(H′) for embedding dimension three (J.O. Kleppe, J. Algebra 200 (1998) 606-628), and the Gotzmann Hilbert scheme theorems (Math. Z. 158(1) (1978) 61-70).