  We show that if the complement of a Donaldson hypersurface in a closed,
integral symplectic manifold has the homology of a subcritical Stein manifold,
then the hypersurface is of degree one. In particular, this demonstrates a
conjecture by Biran and Cieliebak on subcritical polarisations of symplectic
manifolds. Our proof is based on a simple homological argument using ideas of
Kulkarni-Wood.
