\"{U}lrich bundles on cyclic coverings of projective spaces

We prove the existence of \"{u}lrich bundles on cyclic coverings of Pⁿ of arbitrary degree d. Given a relative \"{u}lrich bundle on a complete intersection subvariety, we construct a relative \"{u}lrich bundle on the ambient variety. Using this, we prove that there exists a rank d \"{u}lrich 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 \"{u}lrich bundle on generic cyclic coverings of P².