Minimality and irreducibility of symplectic four-manifolds

Details Minimality and irreducibility of symplectic four-manifolds Minimality and irreducibility of symplectic four-manifolds

2005-09-09

arxiv.org/abs/math/0509204v2

International Mathematics Research Notices 2006 (2006), Article ID 35032, 13 pages.

Mathematics

Symplectic Geometry

final version; cosmetic changes only; to appear in International Mathematics Research Notices

Scientific paper

10.1155/IMRN/2006/35032

We prove that all minimal symplectic four-manifolds are essentially
irreducible. We also clarify the relationship between holomorphic and
symplectic minimality of K\"ahler 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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