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Minimality and irreducibility of symplectic four-manifolds

M. J. D. Hamilton, D. Kotschick

math.SGarXiv:math/0509204

Abstract

We prove that all minimal symplectic four-manifolds are essentially irreducible. We also clarify the relationship between holomorphic and symplectic minimality of Kähler surfaces. This leads to a new proof of the deformation-invariance of holomorphic minimality for complex surfaces with even first Betti number which are not Hirzebruch surfaces.

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