  On a complex manifold, a co-Higgs bundle is a holomorphic vector bundle with
an endomorphism twisted by the tangent bundle. The notion of generalized
holomorphic bundle in Hitchin's generalized geometry coincides with that of
co-Higgs bundle when the generalized complex manifold is ordinary complex.
Schwarzenberger's rank-2 vector bundle on the projective plane, constructed
from a line bundle on the double cover CP^1 \times CP^1 \to CP^2, is naturally
a co-Higgs bundle, with the twisted endomorphism, or "Higgs field", also
descending from the double cover. Allowing the branch conic to vary, we find
that Schwarzenberger bundles give rise to an 8-dimensional moduli space of
co-Higgs bundles. After studying the deformation theory for co-Higgs bundles on
complex manifolds, we conclude that a co-Higgs bundle arising from a
Schwarzenberger bundle with nonzero Higgs field is rigid, in the sense that a
nearby deformation is again Schwarzenberger.
