# 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}
}
• Published 31 August 2017
• Mathematics
• ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
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…
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