Ulrich bundles on cyclic coverings of projective spaces

Abstract

We prove the existence of Ulrich bundles on cyclic coverings of of arbitrary degree d. Given a relatively Ulrich bundle on a complete intersection subvariety, we construct a relatively Ulrich bundle on the ambient variety. As an application, we prove that there exists a rank d Ulrich bundle on a generic cyclic covering of of degree d, provided that the degree of the branch divisor is even. When is odd, we also provide an estimation of the rank of the Ulrich bundle on a generic cyclic covering of .