Kodaira dimension and symplectic sums

Details Kodaira dimension and symplectic sums Kodaira dimension and symplectic sums

2007-01-22

arxiv.org/abs/math/0701617v2

Comment. Math. Helv. 84 (2009), no. 1, 57--85

Mathematics

Symplectic Geometry

Minor changes based on referee's comments. To appear in Comment. Math. Helv. 23 pages

Scientific paper

Modulo trivial exceptions, we show that smoothly nontrivial symplectic sums of symplectic 4-manifolds along surfaces of positive genus are never rational or ruled, and we enumerate each case in which they have Kodaira dimension zero (i.e., are blowups of symplectic 4-manifolds with torsion canonical class). In particular, a symplectic four-manifold of Kodaira dimension zero arises by such a surgery only if it is diffeomorphic to a blowup either of the K3 surface, the Enriques surface, or a member of a particular family of T^2-bundles over T^2 each having b_1=2.

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