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A Remark on the Gromov–Witten–Welschinger Invariants of \({ℂP^3}\# {\overline {ℂP} ^{{3_*}}}\)

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Abstract

We establish a formula for the Gromov–Witten–Welschinger invariants of \({ℂP^3}\# {\overline {ℂP} ^3}\). Using birational transformations and pencils of quadrics, we write some real and complex enumerative invariants of \({ℂP^3}\# {\overline {ℂP} ^3}\) as combinations of enumerative invariants of the blow up of \({ℂP^2}\) at two real points.

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Acknowledgments

The author would like to thank Jianxun Hu for continuous support and encouragement, as well as enlightening discussions, and Jianfeng Wu and Ziteng Li for carefully reading the manuscript. The author is also very grateful to the referee for valuable comments and suggestions on the manuscript, which have allowed him to improve the presentation.

Funding

The research was supported in part by Startup Research Fund of Zhengzhou University under grant 161131003.

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  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, P. R. China

    Yanqiao Ding

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  1. Yanqiao Ding
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Correspondence to Yanqiao Ding.

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The article was submitted by the author for the English version of the journal.

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Ding, Y. A Remark on the Gromov–Witten–Welschinger Invariants of \({ℂP^3}\# {\overline {ℂP} ^{{3_*}}}\). Math Notes 107, 727–739 (2020). https://doi.org/10.1134/S000143462005003X

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  • DOI: https://doi.org/10.1134/S000143462005003X

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