# Polynomially convex embeddings of even-dimensional compact manifolds

@article{Gupta2017PolynomiallyCE, title={Polynomially convex embeddings of even-dimensional compact manifolds}, author={Purvi Gupta and Rasul Shafikov}, journal={ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE}, year={2017} }

We show that, for $k>1$, any $2k$-dimensional compact submanifold of $\mathbb{C}^{3k-1}$ can be perturbed to be polynomially convex and totally real except at a finite number of points. This lowers the known bound on the number of smooth functions required on every $2k$-manifold $M$ to generate a dense subalgebra of $\mathcal{C}(M)$. We also show that the obstruction to isotropic embeddability of all $2k$-dimensional manifolds in $\mathbb{C}^{3k-1}$ does not persist if we allow for K\"ahler…

## 2 Citations

### Polynomially convex embeddings of odd-dimensional closed manifolds

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Abstract It is shown that any smooth closed orientable manifold of dimension 2k+1{2k+1}, k≥2{k\geq 2}, admits a smooth polynomially convex embedding into ℂ3k{\mathbb{C}^{3k}}. This improves by 1…

### odd-dimensional closed

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Given a closed orientable abstract manifold M of odd dimension 2k +1, k ≥ 2, it is natural to look for the least n such that M can be embedded in C with certain prescribed properties. We recall that…

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