Symplectic 4-Manifolds and Algebraic Surfaces [electronic resource] : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 /
Auroux, Denis.author.
Centro internazionale matematico estivo Summer SchoolCorporate Author
C.I.M.E. Summer School(2003 :Cetraro, Italy)
Catanese, Fabrizio.author.
Manetti, Marco.author.
Seidel, Paul.author.
Siebert, Bernd.author.
Smith, Ivan.author.
Tian, Gang.author.
Catanese, Fabrizio.editor.
Tian, Gang.editor.
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.
Bibliographic Level Mode of Issuance: Monograph
Includes bibliographical references.
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.
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.
Algebraic geometry.
Differential geometry.
Functions of complex variables.
Group theory.
Manifolds (Mathematics).
Complex manifolds.
Algebraic Geometry.
Differential Geometry.
Several Complex Variables and Analytic Spaces.
Group Theory and Generalizations.
Manifolds and Cell Complexes (incl. Diff.Topology).
Lecture notes in mathematics