Kodaira dimension and symplectic sums
Symplectic Geometry
2014-10-01 v2 Geometric Topology
Abstract
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.
Cite
@article{arxiv.math/0701617,
title = {Kodaira dimension and symplectic sums},
author = {Michael Usher},
journal= {arXiv preprint arXiv:math/0701617},
year = {2014}
}
Comments
Minor changes based on referee's comments. To appear in Comment. Math. Helv. 23 pages