The algebraic density property for affine toric varieties
The algebraic density property for affine toric varieties
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仿射环面簇的代数密度性质
DOI：
10.1016/j.jpaa.2014.12.017
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Alvaro Liendo
中科院分区：
文献类型：
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作者：
F. Kutzschebauch;M. Leuenberger;Alvaro Liendo
在本文中，我们将代数密度性质推广到相对于某些包含奇异轨迹的封闭子品种不一定平滑的仿射簇。这一性质意味着安德森-伦珀特理论的全纯自同构具有显着的近似结果。我们证明，当且仅当 X∖ Y≠ T 时，仿射复曲面簇 X 满足相对于闭合 T 不变子簇 Y 的代数密度性质。对于复曲面，我们能够对那些拥有强版本代数密度性质（相对于奇异轨迹）的复曲面进行分类。该分类的主要成分是我们对布鲁内拉著名的仿射平面中完全代数向量场分类的等变版本的证明。
In this paper we generalize the algebraic density property to not necessarily smooth affine varieties relative to some closed subvariety containing the singular locus. This property implies the remarkable approximation results for holomorphic automorphisms of the Andersén–Lempert theory. We show that an affine toric variety X satisfies this algebraic density property relative to a closed T-invariant subvariety Y if and only if X∖ Y≠ T. For toric surfaces we are able to classify those which possess a strong version of the algebraic density property (relative to the singular locus). The main ingredient in this classification is our proof of an equivariant version of Brunella's famous classification of complete algebraic vector fields in the affine plane.