Arnold's seminar, Moscow, 8th of April, 2003

Victor Goryunov (joint work with  D.Mond)
"Tjurina and Milnor numbers of matrix singularities"

      We prove  that $\tau=\mu$ for two-parameter families of symmetric
 matrices of any order. We also prove similar claims for two other
closely related matrix classification problems: for arbitrary
square matrices depending on 3 parameters and for even order
skew-symmetric matrices in 5 variables.

     The coincidence of $\tau$ and $\mu$ in all the three classifications
is a particular case of the main result on the relation between these two
numbers for the matrix families in suffciently few variables:

       $$ \tau =\mu -\beta_0 +\beta_1 $$

where $\beta_0, \beta_1$ are the Betti numbers of the complex coming from
the relevant matrix resolution.

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