A CR singular analogue of Severi's theorem

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.

22 pages, accepted to Math. Z, fix hypothesis on Proposition 7.1

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Cited by in corpus (2)

• On CR singular CR images
• CR functions at CR singularities: approximation, extension, and hulls