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摘要翻译：
设X=spec A是特征为0的代数闭域k上的正规仿射簇，域k具有维数为n的环面T的有效作用。设D是正规仿射Z^n-分次区域a上的一个齐次局部幂零导子，使D在X上生成一个由T-作用归一化的K+-作用。我们在两种情况下给出了对(X，D)的完全分类：对于toric变体(n=\dim X)和在n=\dim x-1的情况下。这推广了由Flenner和Zaidenberg引起的曲面的已知结果。作为应用，我们计算了这类变体的齐次Makar-Limanov不变量。特别地，我们展示了一族具有平凡Makar-Limanov不变量的非理性变体。
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英文标题：
《Affine T-varieties of complexity one and locally nilpotent derivations》
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作者：
Alvaro Liendo
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最新提交年份：
2011
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
Let X=spec A be a normal affine variety over an algebraically closed field k of characteristic 0 endowed with an effective action of a torus T of dimension n. Let also D be a homogeneous locally nilpotent derivation on the normal affine Z^n-graded domain A, so that D generates a k_+-action on X that is normalized by the T-action. We provide a complete classification of pairs (X,D) in two cases: for toric varieties (n=\dim X) and in the case where n=\dim X-1. This generalizes previously known results for surfaces due to Flenner and Zaidenberg. As an application we compute the homogeneous Makar-Limanov invariant of such varieties. In particular we exhibit a family of non-rational varieties with trivial Makar-Limanov invariant.
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PDF链接：
https://arxiv.org/pdf/0812.0802
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