仿射复曲面簇的代数密度性质
The algebraic density property for affine toric varieties
摘要：
本文将代数密度性质推广到相对于包含奇异轨迹的闭子簇的不一定光滑的仿射簇。这个性质包含了Andersén-Lempert理论的全纯自同构的显著逼近结果。我们证明了仿射复曲面簇X相对于闭T-不变子簇Y满足这种代数密度性质当且仅当X-Y不同于T。对于复曲面，我们能够对那些具有强代数密度性质（相对于奇异轨迹）的曲面进行分类。在这种分类的主要成分是我们证明的等变版本布鲁内拉的著名分类的完整的代数向量场在仿射平面。
英文摘要：
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 is different from T. For toric surfaces we are able to classify those which posses 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.
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