On the determinantal representations of singular hypersurfaces in P^n Academic Article uri icon

abstract

  • A (global) determinantal representation of projective hypersurface in P^n 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 study the determinantal representations of projective hypersurfaces with arbitrary singularities. Finally, we generalize the results to the case of symmetric/self-adjoint representations, with implications for hyperbolic polynomials and generalized Lax conjecture.

publication date

  • January 1, 2009