Homological properties of associative algebras: the method of helices

Homological properties of associative algebras arising in the theory of helices are studied. A class of noncommutative algebras is introduced in which it is natural (from the viewpoint of the theory of helices) to deform projective spaces and also certain Fano varieties. It is shown that in the case of deformations of the projective plane this approach leads to algebras associated with automorphisms of two-dimensional cubic curves.