The general double cover of P^3 branched along a surface of degree 4, 6, or 8 carries a stable rank 2 Ulrich bundle, with moduli components of dimension 5, 6, and 0.
On the classification of non-big Ulrich vector bundles on fourfolds
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abstract
We give an almost complete classification of non-big Ulrich vector bundles on fourfolds. This allows to classify them in the case of Picard rank one fourfolds, of Mukai fourfolds and in the case of Del Pezzo $n$-folds for $n \le 4$. We also classify Ulrich bundles with non-big determinant on Del Pezzo and Mukai $n$-folds, $n \ge 2$.
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Ulrich bundles on double coverings of projective space
The general double cover of P^3 branched along a surface of degree 4, 6, or 8 carries a stable rank 2 Ulrich bundle, with moduli components of dimension 5, 6, and 0.