Abstract
In this paper, we provide computer-based construction of Ulrich bundles of small ranks over some special cubic fourfolds of small discriminants via deformation theory. First, we construct a simple sheaf whose Chern classes are the same as an Ulrich bundle of the same rank (if exists) as the syzygy sheaf of an Ulrich sheaf on a surface contained in a special cubic fourfold. We observe that a general deformation of this simple sheaf becomes Ulrich in several cases. We also provide some experimental constructions of Ulrich bundles on special cubic fourfolds of small discriminants.
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