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Symplectic 4-manifolds on the Noether line and between the Noether and half Noether lines

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Abstract

We construct simply connected, minimal, symplectic 4-manifolds with exotic smooth structures and each with one Seiberg–Witten basic class up to sign, on the Noether line and between the Noether and half Noether lines by star surgeries introduced by Karakurt and Starkston, and by using complex singularities. We also construct certain configurations of complex singularities in the rational elliptic surfaces geometrically, without using any monodromy arguments. By using these configurations, we give symplectic embeddings of star shaped plumbings inside (some blow-ups of) elliptic surfaces.

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Acknowledgements

I would like to thank Anar Akhmedov for his comments on an earlier draft of this paper and for many helpful discussions. I thank Tian-Jun Li for his comments and pointing out a typo. I am grateful to Çağrı Karakurt and Laura Starkston for many correspondences and their sparing time on my questions. I would like to thank the referee for their constructive and positive remarks which improved this manuscript in great amount. I also acknowledge the financial support and hospitality of the Max Planck Institute for Mathematics, Bonn where most of this work was done during my stay as a postdoctoral fellow.

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  1. Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR, 72701, USA

    Sümeyra Sakallı

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Sakallı, S. Symplectic 4-manifolds on the Noether line and between the Noether and half Noether lines. Geom Dedicata 215, 369–399 (2021). https://doi.org/10.1007/s10711-021-00655-6

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