摘要翻译：
研究了一类多值齐次函数的极性变换的程度。特别地，我们证明了与齐次多项式$F$相关的极变换的泛型线性空间的前像的阶是由$F$的零轨迹决定的。对于零维-维线性空间，这是Dolgachev的猜想，并由Dimca-Papadima利用拓扑变元证明。我们的方法是代数几何的，依赖于对自然关联的对数叶的高斯映射的研究。
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英文标题：
《On the degree of Polar Transformations -- An approach through
  Logarithmic Foliations》
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作者：
Thiago Fassarella, Jorge Vit\'orio Pereira
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最新提交年份：
2007
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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：
  We investigate the degree of the polar transformations associated to a certain class of multi-valued homogeneous functions. In particular we prove that the degree of the pre-image of generic linear spaces by a polar transformation associated to a homogeneous polynomial $F$ is determined by the zero locus of $F$. For zero dimensional-dimensional linear spaces this was conjecture by Dolgachev and proved by Dimca-Papadima using topological arguments. Our methods are algebro-geometric and rely on the study of the Gauss map of naturally associated logarithmic foliations.
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PDF链接：
https://arxiv.org/pdf/0705.1867