An example of two homeomorphic, nondiffeomorphic complete intersection surfaces
Let \(d_ i\in {\mathbb{N}}\), \(d_ i\geq 2\), \(i=1,...,r\). A complete intersection surface of multidegree \((d_ 1,...,d_ r)\) is a nonsingular algebraic surface \(S(d_ 1,...,d_ r)\subset {\mathbb{C}}{\mathbb{P}}^{r+2}\) which is the transversal intersection of r hypersurfaces of degree \(d_ 1,...,d_ r,\) respectively. Any two complete intersection surfaces with the same multidegree are diffeomorphic. The author proves (by using results of Freedman, Donaldson, Friedman and Morgan) that \(S(10,7,7,6,3,3)\subset {\mathbb{C}}{\mathbb{P}}^ 8\) and \(S(9,5,3,3,3,3,3,2,2)\subset {\mathbb{C}}{\mathbb{P}}^{11}\) are homeomorphic, but not diffeomorphic.
scientific article; zbMATH DE number 4160946