## Abstract

Let x ∈ M_{n}(K) satisfy x ^{2} = 0. Let F_{x} be the Springer fiber over x. The components of F_{x} are labeled by standard Young tableaux with two columns. For a Young tableau T with two columns, one can define a numerical invariant ρ(T). The component F_{T} is singular if and only if ρ(T) ≥ 2. In this paper, we construct the stratification of F_{T} for T with ρ(T) = 2, which reflects also the inner structure of the singular locus, and show that such components have equivalent stratifications if and only if they are isomorphic as algebraic varieties and provide the combinatorial procedure which partitions the set of such components into the classes of isomorphic components. We explain why the stratification of F_{T} for T with ρ(T) ≥ 3 is very complex and does not reflect the inner structure of the singular locus.

Original language | English |
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Pages (from-to) | 867-910 |

Number of pages | 44 |

Journal | Transformation Groups |

Volume | 28 |

Issue number | 2 |

DOIs | |

State | Published - Jun 2023 |

### Bibliographical note

Publisher Copyright:© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

## ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology

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