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On the Dimension of the Locus of Determinantal Hypersurfaces by Reichstein, Zinovy; Vistoli, Angelo is a scholarly article available to read on EtoBox.

What is On the Dimension of the Locus of Determinantal Hypersurfaces about?

The characteristic polynomial of an $r$-tuple $(A_1,..., A_r)$ of $n \times n$ matrices is the determinant $\det(x_0 I + x_1 A_1 + ... + x_r A_r)$. We show that if $r$ is at least 3 and $A = (A_1,..., A_r)$ is an $r$-tuple of matrices in general position, then up to conjugacy there are only finitely many $r$-tuples of matrices with the same characteristic polynomial as $A$. Equivalently, the locus of determinantal hypersurfaces of degree $n$ in $P^r$ is irreducible of dimension $(r-1)n^2 + 1$.

Author

Reichstein, Zinovy; Vistoli, Angelo

Published

2016

Language

EN