论文标题
Segre产品的学位和ED度的渐近学
Asymptotics of degrees and ED degrees of Segre products
论文作者
论文摘要
其经典代数学位及其欧几里得距离学位（ED学位），这两个基本不变剂是其经典的代数学位。在本文中，我们研究了这两个Segre产品及其双重品种的渐近行为。我们分析了（超童）高度确定剂的渐近学，即对Segre品种的双重性超曲面。我们提供了关于某些Segre品种的ED稳定度的另一种观点。尽管这种现象是从弗里德兰 - 奥塔维安尼（Friedland-Ottaviani）的公式中得知的，该公式表达了一般张量的奇异矢量元素的数量，但我们的方法提供了几何解释。最后，我们确定了segre产品$ x \ times q_ {n} $的双重品种程度的稳定，其中$ x $是一种投射品种，$ q_n \ subset \ subset \ mathbb {p}^{n+1} $是平滑的Quadric Quadric Hypersurface。
Two fundamental invariants attached to a projective variety are its classical algebraic degree and its Euclidean Distance degree (ED degree). In this paper, we study the asymptotic behavior of these two degrees of some Segre products and their dual varieties. We analyze the asymptotics of degrees of (hypercubical) hyperdeterminants, the dual hypersurfaces to Segre varieties. We offer an alternative viewpoint on the stabilization of the ED degree of some Segre varieties. Although this phenomenon was incidentally known from Friedland-Ottaviani's formula expressing the number of singular vector tuples of a general tensor, our approach provides a geometric explanation. Finally, we establish the stabilization of the degree of the dual variety of a Segre product $X\times Q_{n}$, where $X$ is a projective variety and $Q_n\subset \mathbb{P}^{n+1}$ is a smooth quadric hypersurface.
