Commentarii Mathematici Helvetici
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Published online: 2009-03-31
Kodaira dimension and symplectic sumsMichael Usher (1) University of Georgia, Athens, United States
Modulo trivial exceptions, we show that 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 T2-bundles over T2 each having b1 = 2.
Keywords: Symplectic Kodaira dimension, symplectic sum, torus fibration, symplectic isotopy
Usher Michael: Kodaira dimension and symplectic sums. Comment. Math. Helv. 84 (2009), 57-85. doi: 10.4171/CMH/152