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

ISBN-13: 9783540782780 / Angielski / Miękka / 2008 / 354 str.

Denis Auroux; Fabrizio Catanese; Marco Manetti

Opis

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.

Spis treści

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.

O autorze

Dr. Bernd Siebert ist Rechtsanwalt und Fachanwalt für Bau- und Architektenrecht. Von 2003 bis 2005 war er Mitherausgeber der Zeitschrift "Baurecht und Baupraxis".