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A CR singular analogue of Severi’s theorem

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Abstract

Real-analytic CR functions on real-analytic CR singular submanifolds are not in general restrictions of holomorphic functions, unlike in the CR nonsingular case. We give a simple condition that completely characterizes those quadric CR singular manifolds of codimension 2 in \({\mathbb {C}}^{n+1}\) for which an extension result holds. Consequently, we obtain an extension result for general real-analytic CR singular submanifolds of codimension 2. As applications we give a condition for the flattening of such submanifolds, and we classify CR singular images of CR submanifolds up to second order.

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Authors and Affiliations

  1. Department of Mathematics, Oklahoma State University, Stillwater, OK, 74078, USA

    Jiří Lebl & Alan Noell

  2. Tata Institute of Fundamental Research, Centre for Applicable Mathematics, Bengaluru, 560065, India

    Sivaguru Ravisankar

Authors
  1. Jiří Lebl
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  2. Alan Noell
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  3. Sivaguru Ravisankar
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Correspondence to Sivaguru Ravisankar.

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Lebl, J., Noell, A. & Ravisankar, S. A CR singular analogue of Severi’s theorem. Math. Z. 299, 1607–1629 (2021). https://doi.org/10.1007/s00209-021-02729-3

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