Ülrich bundles on cyclic coverings of projective spaces

A. J. Parameswaran, Jagadish Pine

Published 2024-08-20Version 1

We prove the existence of \"{u}lrich bundles on cyclic coverings of $\mathbb{P}^n$ 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 $\mathbb{P}^2$ with branch divisor of degree $d \cdot k$ such that $d \cdot k$ is even. When $d \cdot k$ is odd, we also give an estimation of the rank of \"{u}lrich bundle on generic cyclic coverings of $\mathbb{P}^2$.