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On a question of Zariski on Zariski surfaces

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Abstract

We give a new method to construct unirational surfaces which may be applied to the following question posed by Zariski in his studies on unirational surfaces. Is any Zariski surface with geometric genus zero rational? Our main result is a negative answer to this question in any characteristic case.

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Acknowledgments

The author thanks the referee for helpful comments. This work was partially supported by the Grant-in-Aid for Japan Society for the Promotion of Science Fellows (21-1111).

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  1. Department of Mathematics, Graduate School of Science, Kobe University, Hyogo, 657-8501, Japan

    Kentaro Mitsui

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  1. Kentaro Mitsui
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Correspondence to Kentaro Mitsui.

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Mitsui, K. On a question of Zariski on Zariski surfaces. Math. Z. 276, 237–242 (2014). https://doi.org/10.1007/s00209-013-1195-0

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