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Surfaces with pg = q = 1, K2 = 6 and Non-birational Bicanonical Maps

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Abstract

Let S be a smooth minimal projective surface of general type with pg(S) = q(S) = 1, K 2 S = 6. We prove that the degree of the bicanonical map of S is 1 or 2. So if S has non-birational bicanonical map, then it is a double cover over either a rational surface or a K3 surface.

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Acknowledgements

Hu would like to thank Meng Chen for his encouragement. Zhang thanks Carlos Rito, Yifan Chen and Songbo Lin for useful communications. The authors also thank the anonymous referee for the suggestions to improve this paper.

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Authors and Affiliations

  1. School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul, 02455, South Korea

    Yong Hu

  2. School of Mathematical Science, University of Science and Technology of China, Hefei, 230026, P. R. China

    Lei Zhang

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  1. Yong Hu
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  2. Lei Zhang
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Correspondence to Yong Hu.

Additional information

The first author was supported by NSFC (Grant No. 11571076), and the second author by NSFC (Grant Nos. 11771260 and 11401358)

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Hu, Y., Zhang, L. Surfaces with pg = q = 1, K2 = 6 and Non-birational Bicanonical Maps. Acta. Math. Sin.-English Ser. 35, 321–337 (2019). https://doi.org/10.1007/s10114-018-7262-z

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  • DOI: https://doi.org/10.1007/s10114-018-7262-z

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