论文标题
部分可观测时空混沌系统的无模型预测
Determinantal characterization of higher secant varieties of minimal degree
论文作者
论文摘要
各种最小程度是投射代数几何形状中的基本对象之一，并且在许多方面都被分类和表征。另一方面，较高的割线类别中也有最小的对象，它们的代数和几何结构似乎与最小程度的品种具有许多相似之处。 我们在本文中证明，最小程度的较高距离品种具有两种类型的决定性呈现，即卷轴类型和Veronese类型。我们的结果概括了Del Pezzo-Bertini的分类，以最小程度的品种。此外，我们表明，对于任何具有较高距离距离较高的距离的光滑投射品种，嵌入线捆绑包将特殊的分解为两个线束，就像那些众所周知的示例中的捆绑包：光滑的Del pezzo品种，Segreies品种，Segreys和2-Veronese品种。
A variety of minimal degree is one of the basic objects in projective algebraic geometry and has been classified and characterized in many aspects. On the other hand, there are also minimal objects in the category of higher secant varieties, and their algebraic and geometric structures seem to share many similarities with those of varieties of minimal degree. We prove in this paper that higher secant varieties of minimal degree have determinantal presentation of two types, i.e. scroll type and Veronese type. Our result generalizes the del Pezzo-Bertini classification for varieties of minimal degree. Also, as a consequence, we show that for any smooth projective variety having higher secant variety of minimal degree, the embedding line bundle admits a special decomposition into two line bundles as so do those of the well-known examples: varieties of minimal degree, smooth del Pezzo varieties, Segre varieties and 2-Veronese varieties.
