Symplectic 4-Manifolds and Algebraic Surfaces: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 (Lecture Notes in Mathematics Book 1938)

Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 will be useful to people working in related areas of mathematics and will become standard references on these topics. The volume is a coherent exposition of an active field of current research focusing on the introduction of new methods for the study of moduli spaces of complex structures on algebraic surfaces, and for the investigation of symplectic topology in dimension 4 and higher. Front Matter....Pages i-xiii Lefschetz Pencils, Branched Covers and Symplectic Invariants....Pages 1-53 Differentiable and Deformation Type of Algebraic Surfaces, Real and Symplectic Structures....Pages 55-167 Smoothings of Singularities and Deformation Types of Surfaces....Pages 169-230 Lectures on Four-Dimensional Dehn Twists....Pages 231-267 Lectures on Pseudo-Holomorphic Curves and the Symplectic Isotopy Problem....Pages 269-341 Back Matter....Pages 343-345