Add to ORKGAbstract. If a real symmetric matrix of linear forms is positive definite at some point, then its determinant defines a hyperbolic hypersurface. In 2007, Helton and Vinnikov proved a converse in three variables, namely that every hyperbolic curve in the projective plane has a definite real symmetric determinantal repre-sentation. The goal of this paper is to give a more concrete proof of a slightly weaker statement. Here we show that every hyperbolic plane curve has a definite determinantal representation with Hermitian matrices. We do this by relating the definiteness of a matrix to the real topology of its minors and extending a construction of Dixon from 1902. Like the Helton-Vinnikov theorem, this implies that every hyperbolic region in...
AbstractDeterminantal representations of algebraic curves are interesting in themselves, and their c...
Let M = (m_{ij}) be an nxn square matrix of integers. For our purposes, we can assume without loss ...
AbstractFor a pair of n×n Hermitian matrices H and K, a real ternary homogeneous polynomial defined ...
The question which equations of hypersurfaces in the complex projective space can be expressed as th...
We prove that for every smooth hyperbolic polynomial h there is another hy-perbolic polynomial q suc...
Helton and Vinnikov showed that every rigidly convex curve in the real plane bounds a spectrahedron....
summary:The numerical range of an $n\times n$ matrix is determined by an $n$ degree hyperbolic terna...
International audienceWe describe a new method for constructing a spectrahedral representation of th...
International audienceWe describe a new method for constructing a spectrahedral representation of th...
AbstractA (global) determinantal representation of projective hypersurface X⊂Pn is a matrix whose en...
I will survey some topics about hyperbolic polynomials and their determinantal representations, and...
There has recently been ample interest in the question of which sets can be represented by linear ma...
Thesis (Ph.D.)--University of Washington, 2022Research in algebraic geometry has interfaces with oth...
We prove a generalization of the Hermitian version of the Helton–Vinnikov determinantal representati...
We prove a generalization of the Hermitian version of the Helton–Vinnikov determinantal representati...
AbstractDeterminantal representations of algebraic curves are interesting in themselves, and their c...
Let M = (m_{ij}) be an nxn square matrix of integers. For our purposes, we can assume without loss ...
AbstractFor a pair of n×n Hermitian matrices H and K, a real ternary homogeneous polynomial defined ...
The question which equations of hypersurfaces in the complex projective space can be expressed as th...
We prove that for every smooth hyperbolic polynomial h there is another hy-perbolic polynomial q suc...
Helton and Vinnikov showed that every rigidly convex curve in the real plane bounds a spectrahedron....
summary:The numerical range of an $n\times n$ matrix is determined by an $n$ degree hyperbolic terna...
International audienceWe describe a new method for constructing a spectrahedral representation of th...
International audienceWe describe a new method for constructing a spectrahedral representation of th...
AbstractA (global) determinantal representation of projective hypersurface X⊂Pn is a matrix whose en...
I will survey some topics about hyperbolic polynomials and their determinantal representations, and...
There has recently been ample interest in the question of which sets can be represented by linear ma...
Thesis (Ph.D.)--University of Washington, 2022Research in algebraic geometry has interfaces with oth...
We prove a generalization of the Hermitian version of the Helton–Vinnikov determinantal representati...
We prove a generalization of the Hermitian version of the Helton–Vinnikov determinantal representati...
AbstractDeterminantal representations of algebraic curves are interesting in themselves, and their c...
Let M = (m_{ij}) be an nxn square matrix of integers. For our purposes, we can assume without loss ...
AbstractFor a pair of n×n Hermitian matrices H and K, a real ternary homogeneous polynomial defined ...