For a given projective variety X, the high rank loci are the closures of the sets of points whose X-rank is higher than the generic one. We show examples of strict inclusion arising from two consecutive high rank loci. Our first example comes from looking at the Veronese surface of plane quartics. Although Piene had already shown an example in which X is a curve, we construct infinitely many curves in ${\mathbb{P}}^4$ for which such strict inclusion appears. For space curves, we give two criteria to check whether the locus of points of maximum rank 3 is finite (possibly empty).

中文翻译：

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严格包含高级位点

对于给定的投射各种X，高级别位点是点的集合，其的封口X秩比一般一个较高。我们展示了由两个连续的高级位点引起的严格包含的例子。我们的第一个例子来自观察平面四次方程的 Veronese 曲面。尽管 Piene 已经展示了一个例子，其中X是一条曲线，我们在${\mathbb{磷}}^4$出现这种严格的包含。对于空间曲线，我们给出了两个标准来检查最大秩为 3 的点的轨迹是否有限（可能为空）。