论文标题
高阶极性和相互极性品种
Higher order polar and reciprocal polar varieties
论文作者
论文摘要
在本说明中，我们将高阶极性基因座作为经典极地基因座的自然概括，用高阶悬浮空间代替切线空间的作用。极性基因座和双重品种之间的紧密联系将高阶极性基因座与高阶双重品种之间的联系。我们将各种二元等级的二元性与其双重品种的二元性概括为反射到更高顺序的品种。特别是，顶部（最高的）极级k的极性k的程度等于k-th双重品种的程度。我们定义高阶欧几里得正常束，并使用它们来定义高阶相互极性基因座和类。在某些特殊情况下，我们举例说明了如何计算高阶极性和相互极性类别的程度：曲线，卷轴和曲折品种。
In this note we introduce higher order polar loci as natural generalizations of the classical polar loci, replacing the role of tangent spaces by that of higher order osculating spaces. The close connection between polar loci and dual varieties carries over to a connection between higher order polar loci and higher order dual varieties. We generalize the duality between the degrees of polar classes of a variety and those of its dual variety to varieties that are reflexive to a higher order. In particular, the degree of the top (highest codimension) polar class of order k is equal to the degree of the k-th dual variety. We define higher order Euclidean normal bundles and use them to define higher order reciprocal polar loci and classes. We give examples of how to compute the degrees of the higher order polar and reciprocal polar classes in some special cases: curves, scrolls, and toric varieties.
