As already announced in Cetraro at the beginning of the C.I.M.E. course, we deflected from the broader target ‘Classification and deformation types of complex and real manifolds’, planned and announced originally.
In lecture three we show first that deformation equivalence implies diffeomorphism, and then, using a result concerning symplectic approximations of projective varieties with isolated singularities and Moser's theorem, we show that a surfaces of general type has a ‘canonical symplectic structure’, i.e., a symplectic structure whose class is the class of the canonical divisor, and which is unique up to symplectomorphism.
In lecture three and the following ones we thus enter ‘in medias res’, since one of the main problems that we discuss in these Lecture Notes is the comparison of differentiable and deformation type of minimal surfaces of general type, keeping also in consideration the canonical symplectic structure (unique up to symplectomorphism and invariant for smooth deformation) which these surfaces possess.
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Catanese, F. (2008). Differentiable and Deformation Type of Algebraic Surfaces, Real and Symplectic Structures. In: Catanese, F., Tian, G. (eds) Symplectic 4-Manifolds and Algebraic Surfaces. Lecture Notes in Mathematics, vol 1938. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78279-7_2
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