Abstract
We introduce the notion of biregular index models (infinite series) of orbifold del Pezzo surfaces having their (sub) anti-canonical embeddings in some weighted projective space P ( w i ) . We construct such models of del Pezzo surface with embeddings in P 6 ( w i ) containing at worst rigid orbifold points. The equations describing their images under their (sub) anti-canonical embeddings can be computed by using equations of the Segre embedding of P 1 × P 1 × P 1 in P 7 ; giving rise to codimension 4 Gorenstein varieties. We also compute a formula for the Hilbert series of a general weighted P 1 × P 1 × P 1 ⏧ P 7 ( w i ) variety that plays a pivotal role in these constructions.
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