Canonical symplectic structures and deformations of algebraic surfaces

2006/08/04 by Fabrizio Catanese, Catanese, Fabrizio · 1 citation
Mathematics · #14J10 #14J15 #14J17 #14J29 #53D05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.math/0608110

openalex publication_date 2006/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that a minimal surface of general type has a canonical symplectic structure (unique up to symplectomorphism) which is invariant for smooth deformation. We show that the symplectomorphism type is also invariant for deformations which allow certain normal singularities, provided one remains in the same smoothing component. We use this technique to show that the Manetti surfaces yield examples of surfaces of general type which are not deformation equivalent but are canonically symplectomorphic.

Cited by

• A new coding theory, for normal surfaces, and ADE singularities, I

Related

• Symplectic structures of algebraic surfaces and deformation
• Diffeomorphism of simply connected algebraic surfaces
• Symplectic log Calabi-Yau surface---deformation class
• Differentiable and deformation type of algebraic surfaces, real and symplectic structures
• On deformations of Q-factorial symplectic varieties