A complete intersection is an algebraic variety cut out by homogenous polynomials. Geometrically, this is the intersection of hypersurfaces in complex projective space.
Below, let's confine to the non-singluar case. These are smooth manifolds and much topological information could be read out from the degrees of the polynomials used. see wikipedia
and manifold atlas
for a survey.
I am interested in the
smooth structures on the homeomorphism types of complete intersection.
In particular, are there two complete intersections which are homeomorphic but not diffeomorphic? In the paper
An example of two homeomorphic, nondiffeomorphic complete intersection surfaces. Invent. Math. 99 (1990), no. 3, 651–654.
Wolfgang Ebeling gave an example in the surface case. How about higher dimensions?