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An example of two homeomorphic, nondiffeomorphic complete intersection surfaces. (English) Zbl 0707.14045
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.
Reviewer: T.Krasiński

##### MSC:
 14M10 Complete intersections 57R50 Differential topological aspects of diffeomorphisms 14J10 Families, moduli, classification: algebraic theory 14N05 Projective techniques in algebraic geometry
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##### References:
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