Symplectic 4-Manifolds and Algebraic Surfaces

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003
2008
ISBN: 978-3-540-78278-0
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 354 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1150 g

Reihe: C.I.M.E. Foundation Subseries

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.

Zielgruppe

Research

Autoren/Hrsg.

Auroux, Denis

Manetti, Marco

Catanese, Fabrizio

Smith, Ivan

Seidel, Paul

Tian, Gang

Siebert, Bernd

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
• Mathematik | Informatik Mathematik Topologie Analytische Topologie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

Lefschetz Pencils, Branched Covers and Symplectic Invariants.- Differentiable and Deformation Type of Algebraic Surfaces, Real and Symplectic Structures.- Smoothings of Singularities and Deformation Types of Surfaces.- Lectures on Four-Dimensional Dehn Twists.- Lectures on Pseudo-Holomorphic Curves and the Symplectic Isotopy Problem.