Automorphisms of Certain Projective Bundles over Toric Varieties

The purpose of this note is to exhibit the automorphism group of a projective bundle P(E) over a simplicial toric variety X when the bundle E is a direct sum of equvariant line bundles. This case is important in the study of moduli of complete intersections on toric varieties including projective spaces. The main result is that the automorphism group of P (E) is, up to a finite group, the semi-direct product of the automorphism group of the base and a certain subgroup of fiber preserving automorphisms. This structure is similar to the structure of the automorphism groups of rational surfaces Fn (see [5] p. 425) Applications to moduli space constructions are indicated in special cases, including Del Pezzo surfaces and certain Calabi Yau m-folds.