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

Jongil Park

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

Jongil Park

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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.

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Jongil Park. 2001-08-31. Non-complex symplectic 4-manifolds with $b_{2}^{+}=1$. https://arxiv.org/abs/math/0108220

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