The cohomology and intersection form of smooth hypersurfaces in weighted projective spaces are computed explicitly via Alexander duality and a covering by ordinary projective space.
Homotopy properties of algebraic sets
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Cohomology of hypersurfaces of weighted projective space and the intersection form on $H^2$
The cohomology and intersection form of smooth hypersurfaces in weighted projective spaces are computed explicitly via Alexander duality and a covering by ordinary projective space.