Subcritical polarisations of symplectic manifolds have degree one
arXiv:2101.02068 · doi:10.1007/s00013-021-01605-0
Abstract
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.
arXiv comment4 pages