In this paper, we show that if a vector bundle of rank $n-1$ on projective $(n-1)$-space is very ample and if its top Chern class is greater than one, then the discriminant locus of the vector bundle, the locus of singular sections of the vector bundle, is an irreducible hypersurface and that the degree of the hypersurface can be expressed as a function of invariants of the vector bundle. As applications, we study the eigendiscriminant locus (the locus of tensors whose eigenschemes are singular) and the discriminant locus of the generic graded matrix (the locus of singular determinantal schemes).

中文翻译：

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在$ \ mathbb P ^ {n-1} $上的秩$ n-1 $向量束的判别轨迹上

在本文中，我们表明，如果射影$（n-1）$-空间上的秩为$ n-1 $的向量束非常充足，并且其最高Chern类大于1，则该向量的判别轨迹向量束，向量束奇异段的轨迹，是不可约的超曲面，并且超曲面的程度可以表示为向量束的不变性的函数。作为应用，我们研究本征判别轨迹（本征特征为单数的张量轨迹）和通用分级矩阵的判别轨迹（奇异行列式方案的轨迹）。