Determinantal representations of singular hypersurfaces in Pn

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18 Scopus citations


A (global) determinantal representation of projective hypersurface X Pn is a matrix whose entries are linear forms in homogeneous coordinates and whose determinant defines the hypersurface. We study the properties of such representations for singular (possibly reducible or non-reduced) hypersurfaces. In particular, we obtain the decomposability criteria for determinantal representations of globally reducible hypersurfaces. Further, we classify the determinantal representations in terms of the corresponding kernel sheaves on X. Finally, we extend the results to the case of symmetric/self-adjoint representations, with implications to hyperbolic polynomials and the generalized Lax conjecture.

Original languageEnglish
Pages (from-to)1619-1654
Number of pages36
JournalAdvances in Mathematics
Issue number3-4
StatePublished - 1 Oct 2012


  • Arithmetically Cohen-Macaulay sheaves
  • Determinantal hypersurfaces
  • Hyperbolic polynomials
  • Primary
  • Secondary

ASJC Scopus subject areas

  • Mathematics (all)


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