Canonical symplectic structures and deformations of algebraic surfaces

Details Canonical symplectic structures and deformations of algebraic surfaces Canonical symplectic structures and deformations of algebraic surfaces

2006-08-04

arxiv.org/abs/math/0608110v2

Mathematics

Algebraic Geometry

13 pages, one figure. Some theorems are slightly reformulated, the introduction has been changed and is more informative, a pi

Scientific paper

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.

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