Symplectic 4-Manifolds and Algebraic Surfaces: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy September 2–10, 2003

Denis Auroux, Marco Manetti, Paul Seidel, Bernd Siebert, Ivan Smith (auth.), Fabrizio Catanese, Gang Tian (eds.)9783540782780, 3540782788, 3540782796

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.

Table of contents :
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