Weak Brill-Noether bundles on nodal Enriques surfaces

We study the weak Brill–Noether problem for vector bundles on nodal Enriques surfaces by exploiting the classical realization of a nodal Enriques surface $X$ as a Reye congruence in the Grassmannian $\mathrm{Gr}(2,4)$. We consider restrictions of irreducible homogeneous bundles from the ambient Grassmannian and study their behavior with respect to the weak Brill–Noether property and slope stability.