We prove the existence of an abundance of new Einstein metrics on odd
dimensional spheres including exotic spheres, many of them depending on
continuous parameters. The number of families as well as the number of
parameter grows double exponentially with the dimension. Our method of proof
uses Brieskorn-Pham singularities to realize spheres (and exotic spheres) as
circle orbi-bundles over complex algebraic orbifolds, and lift a
Kaehler-Einstein metric from the orbifold to a Sasakian-Einstein metric on the
sphere.Comment: 19 pages, some references added and clarifications made. to appear in
Annals of Mathematic
