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On the Dimension of the Locus of Determinantal Hypersurfaces

  • Zinovy Reichstein (a1) and Angelo Vistoli (a2)
Abstract

The characteristic polynomial PA (x 0 , . . . , xr ) of an r-tuple A := (A 1 , . . . , Ar ) of n×n-matrices is defined as

We show that if r E h and A := (A1 , . . . , Ar) is an r-tuple of n × n-matrices in general position, then up to conjugacy, there are only ûnitely many r-tuples A' := (A'1 , . . . , A' r) such that pA = pA ' . Equivalently, the locus of determinantal hypersurfaces of degree n in P r is irreducible of dimension (r − 1)n 2 + 1.

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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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