TITULO
Miniversal Deformations of Marked Matrices

AUTOR

Albert Compta, Josep Ferrer and Ferran Puerta

Departament de Matem\`{a}tica Aplicada I.\\
E.T.S. Ingenieria Industrial de Barcelona. UPC\\
Diagonal 647. 08028 Barcelona. Spain\\
e-mails: compta@ma1.upc.es, ferrer@ma1.upc.es, puerta@ma1.upc.es}%}


ABSTRACT

Given the set of square matrices $\mathcal{M}\subset
M_{n+m}(\w{C})$ that keep the subspace $W=\w{C}^n \mbox{x} \{0\}
\subset \w {C}^{n+m}$ invariant, we obtain the implicit form of a
miniversal deformation of a matrix $a \in \mathcal{M}$, and we
compute it explicitely when this matrix is marked (this is, if
there is a permutation matrix $p \in M_{n+m}(\w {C})$ such that
$p^{-1}ap$ is a Jordan matrix). We derive some applications to
tackle the classical Carlson problem.