Differentiable and deformation type of algebraic surfaces, real and symplectic structures

TL;DR

This paper explores the classification, deformation, and symplectic structures of algebraic surfaces, focusing on their differentiable and deformation types, and their relation to complex and symplectic geometry.

Contribution

It provides a comprehensive overview of the deformation and symplectic classification of algebraic surfaces, highlighting new insights into their diffeomorphism and symplectomorphism types.

Findings

Canonical symplectic structures for surfaces of general type

Deformation and diffeomorphism classifications of algebraic surfaces

Connections between complex, symplectic, and topological properties

Abstract

Lecture 1: Projective and K\"ahler Manifolds, the Enriques classification, construction techniques. Lecture 2: Surfaces of general type and their Canonical models. Deformation equivalence and singularities. Lecture 3: Deformation and diffeomorphism, canonical symplectic structure for surfaces of general type. Lecture 4: Irrational pencils, orbifold fundamental groups, and surfaces isogenous to a product. Lecture 5: Lefschetz pencils, braid and mapping class groups, and diffeomorphism of ABC-surfaces. Epilogue: Deformation, diffeomorphism and symplectomorphism type of surfaces of general type.