Differentiable and Deformation Type of Algebraic Surfaces, Real and Symplectic Structures

Abstract

Lecture 1: Projective and K\ahler Manifolds, the Enriques classification, construction techniques. Lecture 2: Surfaces of general type and their Canonical models. Deformation equivalence and singularities. Lecture 3: Deformation and diffeomorphism, canonical symplectic structure for surfaces of general type. Lecture 4: Irrational pencils, orbifold fundamental groups, and surfaces isogenous to a product. Lecture 5: Lefschetz pencils, braid and mapping class groups, and diffeomorphism of ABC-surfaces. Epilogue: Deformation, diffeomorphism and symplectomorphism type of surfaces of general type.