2016/11/04 by Kaliman, Shulim, Kutzschebauch, Frank, Truong, Tuyen Trung
#14R20 #32M17 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1611.01311
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 Xi of a finite number of Zariski open sets, each Xi being quasi-affine, so that there is a positive integer N for which Xi× ℂN 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.