Advanced Search

We consider the Springer fiber ${ℬ}_u$ corresponding to a nilpotent endomorphism $u$ of nilpotent order $2$. As a first result, we give a description of the elements of a given component of ${ℬ}_u$ which are fixed by the action of the standard torus relative to some Jordan basis of $u$. By using this result, we establish a necessary and sufficient condition of singularity for the components of ${ℬ}_u$.