Symplectic structures of algebraic surfaces and deformation

We show that a surface of general type has a canonical symplectic structure (up to symplectomorphism) which is invariant for smooth deformation. Our main theorem is that the symplectomorphism type is also invariant for deformations which also allow certain normal singularities, called Single Smoothing Singularities ( and abbreviated as SSS), or yielding Q-Gorenstein smoothings of quotient singularities. Using the counterexamples of M.Manetti to the DEF = DIFF question whether deformation type and diffeomorphism type coincide for algebraic surfaces, we show that these yield surfaces of general type which are not deformation equivalent but are symplectomorphic. In particular, they are diffeomorphic through a diffeomorphism carrying the canonical class of one to the canonical class of the other surface. ii) Another interesting corollary is the existence of cuspidal algebraic plane curves which are symplectically isotopic, but not equisingular deformation equivalent. The research of the author was performed in the realm of the SCHWERPUNKT ”Globale Methode in der komplexen Geometrie”, and of the EAGER EEC Project.