Kodaira dimension and symplectic sums

Michael Usher
2009 Commentarii Mathematici Helvetici  
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
more » ... r of a particular family of T 2 -bundles over T 2 each having b 1 = 2. 1991 Mathematics Subject Classification. Primary 57R17; Secondary 53D35, 57R57.
doi:10.4171/cmh/152 fatcat:x7247374sfef5lttdfb65nshii