Some wonderful rings in algebraic geometry

Abstract

Let A = k ⊕ A 1… be a graded ring over a field k. The ring is wonderful if Tor A i ( k, k) has pure degree i for all i where k = A A 1 . In a previous paper [4] it was discovered that the ring of regular functions on many cones over abelian varieties is wonderful. Similarly in [1]Backelin has shown that embeddings by high enough trists on ample sheaf on projective schemes give wonderful rings. We will estimate “high enough” and we will note that the coordinate ring of Grassmannians in Plücker coordinates gives wonderful rings. More exactly.