Degeneracy and perturbation conjecture for isolated complex tangents

Let M3C3M^3\hookrightarrow\mathbb{C}^3 be an embedding, and suppose it has an isolated complex tangent. Isolated complex tangent conjecture. Every isolated complex tangent of the embedding is necessarily degenerate. Moreover, a sufficiently small perturbation resolves it into either an elliptic circle or a hyperbolic circle. The conjecture concerns the local behavior of isolated complex tangencies in real three-dimensional submanifolds of C3\mathbb{C}^3. The source gives no resolution status or further evidence.

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Primary source

Ali M. Elgindi, “Holomorphic Hulls for Compact 3-Manifolds”, arXiv:2606.24951 (2026).

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