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A curve-detecting formula for projective surfaces

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Abstract

We present an intersection-theoretic formula concerning curves on projective surfaces in terms of lattices with special emphasis on minimal resolutions of \({\mathbb {Q}}\)-homology projective planes. This formula can be used to detect the existence/nonexistence of curves with given intersection properties.

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Acknowledgements

The author would like to thank the referee for the careful reading and suggestions which improved the exposition of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Ajou University, Suwon, 16499, Republic of Korea

    DongSeon Hwang

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  1. DongSeon Hwang
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Correspondence to DongSeon Hwang.

Additional information

This research was supported by the Samsung Science and Technology Foundation under Project SSTF-BA1602-03.

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Hwang, D. A curve-detecting formula for projective surfaces. European Journal of Mathematics 5, 903–908 (2019). https://doi.org/10.1007/s40879-018-0240-2

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  • DOI: https://doi.org/10.1007/s40879-018-0240-2

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