On subelliptic manifolds
| Autor: | Frank Kutzschebauch, Tuyen Trung Truong, Shulim Kaliman |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Subvariety Group (mathematics) General Mathematics 010102 general mathematics Algebraic variety 14R20 32M17 Equidimensional Unipotent 01 natural sciences Mathematics - Algebraic Geometry 510 Mathematics 0103 physical sciences FOS: Mathematics Affine space 010307 mathematical physics 0101 mathematics Algebraic number Variety (universal algebra) Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | Kaliman, Shulim; Kutzschebauch, Frank; Truong, Tuyen Trung (2018). On subelliptic manifolds. Israel journal of mathematics, 228(1), pp. 229-247. Springer 10.1007/s11856-018-1760-7 |
| DOI: | 10.7892/boris.125524 |
| Popis: | 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. Comment: dedicated to Mikhail Zaidenberg on the Occasion of his 70-th birthday, new stronger results included, coauthor added, some partial results removed |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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