Higher Gauss Maps of Veronese Varieties-a generalization of Boole's formula
Higher Gauss Maps of Veronese Varieties-a generalization of Boole's formula
复制标题
维罗纳品种的高斯图——布尔公式的推广
DOI：
10.1080/00927872.2018.1435790
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发表时间：
2018
影响因子：
0.7
通讯作者：
Hajime
中科院分区：
文献类型：
--
作者：
KAJI;Hajime
讨论了射影簇的高斯图的图像。这里的高斯图概念是由 Fyodor L. Zak 引入的，作为普通高斯图和共法图的推广。主要结果是维罗纳品种的图像程度的封闭公式。这产生了乔治·布尔 (George Boole) 在 1844 年关于维罗纳变体的双变体度的经典公式的推广。作为我们公式的应用，给出了维罗纳变体的高斯图图像的度范围。
The image of the higher Gauss map for a projective variety is discussed. The notion of higher Gauss maps here was introduced by Fyodor L. Zak as a generalization of both ordinary Gauss maps and conormal maps. The main result is a closed formula for the degree of those images of Veronese varieties. This yields a generalization of a classical formula by George Boole on the degree of the dual varieties of Veronese varieties in 1844. As an application of our formula, degree bounds for higher Gauss map images of Veronese varieties are given.