\"Ulrich bundles on cyclic coverings of projective spaces

We prove the existence of \"ulrich bundles on cyclic coverings of Pⁿ of arbitrary degree d. Given a relative \"ulrich bundle on a complete intersection subvariety, we construct a relative \"ulrich bundle on the ambient variety. Using this, we prove that there exists a rank d \"ulrich bundle on degree d generic cyclic coverings of P² with branch divisor of degree d k such that d k is even. When d k is odd, we also give an estimation of the rank of \"ulrich bundle on generic cyclic coverings of P².