  Let $R$ be a hypersurface in an equicharacteristic or unramified regular
local ring. For a pair of modules $(M,N)$ over $R$ we study applications of
rigidity of $\Tor^R(M,N)$, based on ideas by Huneke, Wiegand and Jorgensen. We
then focus on the hypersurfaces with isolated singularity and even dimension,
and show that modules over such rings behave very much like those over regular
local rings. Connections and applications to projective hypersurfaces such as
intersection dimension of subvarieties and cohomological criterion for
splitting of vector bundles are discussed.
