Abstract
We consider the problem of projectively embedding strictly pseudoconcave surfaces, X_ containing a positive divisor, Z and affinely embedding its 3-dimensional, strictly pseudoconvex boundary, \( M = - bX\_ \) We show that embeddability of M in affine space is equivalent to the embeddability of X_ or of appropriate neighborhoods of Z inside X_ in projective space. Under the cohomological hypotheses: \( H_{comp}^2\left( {{X_ - },\left( - \right)} \right) = 0 \) And \( {H^1}\left( {Z,{N_Z}} \right) = 0 \) these embedding properties are shown to be preserved under convergence of the complex structures in the C ∞-topology.
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Epstein, C.L., Henkin, G.M. (2000). Embeddings for 3-dimensional CR-manifolds. In: Dolbeault, P., Iordan, A., Henkin, G., Skoda, H., Trépreau, JM. (eds) Complex Analysis and Geometry. Progress in Mathematics, vol 188. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8436-5_18
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DOI: https://doi.org/10.1007/978-3-0348-8436-5_18
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