In mathematics, Dolgachev surfaces are certain simply connected elliptic surfaces, introduced by Igor Dolgachev (1981).
They can be used to give examples of an infinite family of homeomorphic simply connected compact 4-manifolds, no two of which are diffeomorphic.
of the projective plane in 9 points can be realized as an elliptic fibration all of whose fibers are irreducible.
A Dolgachev surface
is given by applying logarithmic transformations of orders 2 and q to two smooth fibers for some
The Dolgachev surfaces are simply connected, and the bilinear form on the second cohomology group is odd of signature
Simon Donaldson (1987) found the first examples of simply-connected homeomorphic but not diffeomorphic 4-manifolds
More generally the surfaces
Selman Akbulut (2012) showed that the Dolgachev surface