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Well-Formedness vs Weak Well-Formedness

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Abstract

The literature contains two definitions of well formed varieties in weighted projective spaces. By the first, a variety is well formed if its intersection with the singular locus of the ambient weighted projective space has codimension at least 2. By the second, a variety is well formed if it does not include a singular stratum of the ambient weighted projective space in codimension 1. We show that these two definitions differ indeed, and show that they coincide for the quasismooth weighted complete intersections of dimension at least 3.

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References

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Acknowledgments

This article is a byproduct of working on the book Weighted Complete Intersections by the author and C. Shramov. I am grateful to him for the discussions without which this article would not be written.

Funding

This work was supported by the Russian Science Foundation under Grant no. 19–11–00164; https://rscf.ru/ project/19-11-00164/.

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Authors and Affiliations

  1. Steklov Mathematical Institute, Moscow, Russia

    V. V. Przyjalkowski

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  1. V. V. Przyjalkowski
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Correspondence to V. V. Przyjalkowski.

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 4, pp. 786–793. https://doi.org/10.33048/smzh.2023.64.411

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Przyjalkowski, V.V. Well-Formedness vs Weak Well-Formedness. Sib Math J 64, 890–896 (2023). https://doi.org/10.1134/S0037446623040110

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  • DOI: https://doi.org/10.1134/S0037446623040110

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