On subelliptic manifolds

Shulim Kaliman; Frank Kutzschebauch; Tuyen Trung Truong

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arXiv · 1611.01311

On subelliptic manifolds

Shulim Kaliman·Frank Kutzschebauch·Tuyen Trung Truong

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Abstract

A smooth complex quasi-affine algebraic variety $Y$ is flexible if its special group $\SAut (Y)$ of automorphisms (generated by the elements of one-dimensional unipotent subgroups of $\Aut (Y)$) acts transitively on $Y$. An irreducible algebraic manifold $X$ is locally stably flexible if it is the union $\bigcup X_i$ of a finite number of Zariski open sets, each $X_i$ being quasi-affine, so that there is a positive integer $N$ for which $X_i\times \mathbb{C}^N$ is flexible for every $i$. The main result of this paper is that the blowup of a locally stably flexible manifold at a smooth algebraic submanifold (not necessarily equi-dimensional or connected) is subelliptic, and hence Oka. This result is proven as a corollary of some general results concerning the so-called $k$-flexible manifolds.

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BibTeX RIS

Shulim Kaliman, Frank Kutzschebauch, Tuyen Trung Truong. 2016-11-04. On subelliptic manifolds. https://arxiv.org/abs/1611.01311

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