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Kodaira dimension of fiber sums along spheres

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In this note we discuss the effect of the symplectic sum along spheres in symplectic four-manifolds on the Kodaira dimension of the underlying symplectic manifold. We find that the Kodaira dimension is non-decreasing. Moreover, we are able to obtain precise results on the structure of the manifold obtained from the blow down of an embedded symplectic \(-4\)-sphere.

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Acknowledgments

I gratefully acknowledge the patient support of my advisor Prof. Tian Jun Li. I also would like to thank Prof. Bob Gompf for pointing out Lemma 3.6 and describing the underlying method. I also thank Weiyi Zhang and Weiwei Wu for their interest. Thanks also to an anonymous referee for making me aware of a gap in the proof of Lemma 3.14. Part of this work was completed at the University of Minnesota and while at the Graduiertenkolleg 1463: Analysis, Geometry and String Theory in Hannover. The author is partially supported by a Grant from the Simons Foundation (\(\#\)246043).

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  1. Department of Mathematics, North Dakota State University, Dept #2750, PO Box 6050, Fargo, ND , 58108-6050, USA

    Josef G. Dorfmeister

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  1. Josef G. Dorfmeister
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Dorfmeister, J.G. Kodaira dimension of fiber sums along spheres. Geom Dedicata 177, 1–25 (2015). https://doi.org/10.1007/s10711-014-9974-2

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