JournalscmhVol. 84 , No. 1DOI 10.4171/cmh/152

Kodaira dimension and symplectic sums

  • Michael Usher

    University of Georgia, Athens, United States
Kodaira dimension and symplectic sums cover


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.