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arXiv · 0906.3012

Determinantal representations of singular hypersurfaces in P^n

Dmitry Kerner·Victor Vinnikov
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Abstract

A (global) determinantal representation of 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 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 generalized Lax conjecture.

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Dmitry Kerner, Victor Vinnikov. 2009-06-16. Determinantal representations of singular hypersurfaces in P^n. https://arxiv.org/abs/0906.3012

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