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arXiv · 1311.2424

On singularities in B-orbit closures of 2-nilpotent matrices

Martin Bender
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Abstract

This paper deals with singularities of closures of $2$-nilpotent Borel conjugacy classes in either a $\text{GL}_n$-conjugacy class or in the nilpotent cone of $\text{GL}_n$. In the latter case we construct a resolution of singularities, in the former we show that singularities are rational by applying a result of M. Brion. We reason why this generalizes the result of N. Perrin and E. Smirnov on the rationality of singularities of Springer fiber components in the two-column case. In the case of Borel orbit closures being contained in orbital varieties, we give an alternative version of L. Fresse's recent singularity criterion.

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Martin Bender. 2013-11-26. On singularities in B-orbit closures of 2-nilpotent matrices. https://arxiv.org/abs/1311.2424

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