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arXiv · 1909.04752

A CR singular analogue of Severi's theorem

Jiri Lebl·Alan Noell·Sivaguru Ravisankar
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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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Jiri Lebl, Alan Noell, Sivaguru Ravisankar. 2019-09-10. A CR singular analogue of Severi's theorem. https://doi.org/10.1007/s00209-021-02729-3

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