Non-complex symplectic 4-manifolds with $b_{2}^{+}=1$

Jongil Park

paper

Non-complex symplectic 4-manifolds with $b_{2}^{+} = 1$

arXiv:math/0108220

Abstract

In this short article we give a criterion whether a given minimal symplectic 4-manifold with $b_{2}^{+} = 1$ having a torsion-free canonical class is rational or ruled. As a corollary, we confirm that most of homotopy elliptic surfaces $E(1}_{K}$, K is a fibered knot in $S^{3}$ , constructed by R. Fintushel and R. Stern are minimal symplectic 4-manifolds with $b_{2}^{+} = 1$ which do not admit a complex structure.

AMS-LaTeX file, 7 pages

Non-complex symplectic 4-manifolds with b2+​=1

Abstract

Non-complex symplectic 4-manifolds with $b_{2}^{+} = 1$