Given a nilpotent endomorphism, we consider the manifold of invariant subspaces having
a fixed Segre characteristic. In [Linear Algebra Appl., 332–334 (2001) 569], the implicit form
of a miniversal deformation of an invariant subspace with respect to the usual equivalence
relation between subspaces is obtained. Here we obtain the explicit form of this deformation
when the invariant subspace is marked, and we use it to calculate the dimension of the orbit and
in particular to characterize the stable marked subspaces (those with open orbit).Moreover, we
study the rank of the endomorphisms in the quotient space by the subspaces in the miniversal
deformation of the giving subspace.
CitationCompta Creus, Albert; Ferrer Llop, Josep; Peña Carrera, Marta. "Dimension of the orbit of marked subspaces". Linear algebra and its applications, 2004, núm. 379, p. 239-248.
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