For x ∈ End(𝕂ⁿ) satisfying x² = 0 let ℱ_x be the variety of full flags stable under the action of x (Springer fiber over x). The full classification of the components of ℱ_x according to their smoothness was provided in [4] in terms of both Young tableaux and link patterns. Moreover in [2] the purely combinatorial algorithm to compute the singular locus of a singular component of ℱ_x is provided. However, this algorithm involves the computation of the graph of the component, and the complexity of computations grows very quickly, so that in practice it is impossible to use it. In this paper, we construct another algorithm, giving all the components of the singular locus of a singular component ℱ_σ of ℱ_x in terms of link patterns constructed straightforwardly from the link pattern of σ.

对于满足x ^{2 = 0 的}x ∈ End(𝕂 ⁿ )令 ℱ _x是在x的作用下稳定的完整标志的变体（Springer 纤维在x上）。在 [4] 中根据 Young tableaux 和链接模式提供了根据平滑度对 ℱ _{x的分量进行的完整分类。此外，在 [2] 中，计算 ℱ x}的奇异分量的奇异轨迹的纯组合算法提供。但是，该算法涉及到组件图的计算，计算的复杂度增长很快，在实际应用中是不可能的。在本文中，我们构造了另一种算法，根据直接从 σ 的链接模式构造的链接模式，给出 ℱ _{x的奇异分量 ℱ σ的奇异轨迹的所有分量。}