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On the formal principle for curves on projective surfaces

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Abstract

We prove that the formal completion of a complex projective surface along a rigid smooth curve with trivial normal bundle determines the birational equivalence class of the surface.

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Acknowledgements

J.V. Pereira thanks Jun-Muk Hwang for calling his attention to the literature on the formal principle. Both J.V. Pereira and O. Thom are grateful to Frank Loray for helpful discussions and to the anonymous referee for the careful reading and thoughtful suggestions. J. V. Pereira was supported by Cnpq and FAPERJ. O. Thom was supported by Cnpq. Both authors acknowledge support from CAPES-COFECUB Ma932/19 project.

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  1. Instituto Nacional de Matematica Pura e Aplicada Rio de Janeiro, Rio de Janeiro, Brazil

    Jorge Vitório Pereira & Olivier Thom

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  1. Jorge Vitório Pereira
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  2. Olivier Thom
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Correspondence to Olivier Thom.

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Communicated by Ngaiming Mok.

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Pereira, J.V., Thom, O. On the formal principle for curves on projective surfaces. Math. Ann. 381, 1869–1883 (2021). https://doi.org/10.1007/s00208-020-02085-3

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  • DOI: https://doi.org/10.1007/s00208-020-02085-3

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