Horn's Problem, Vinnikov Curves and the Hive Cone
| dc.creator | Speyer, David E | |
| dc.date | 2003-11-25 | |
| dc.date.accessioned | 2026-07-07T05:03:13Z | |
| dc.date.available | 2026-07-07T05:03:13Z | |
| dc.description | A Vinnikov curve is a projective plane curve which can be written in the form det(xX+yY+zZ)=0 for X, Y and Z positive definite Hermitian n by n matrices. Given three n-tuples of positive real numbers, alpha, beta and gamma, there exist A, B and C in GL_n \CC with singular values alpha, beta and gamma and ABC=1 if and only if there is a Vinnikov curve passing through the 3n points (-1: alpha_i^2:0), (0:-1:beta_i^2) and (gamma_i^2:0:-1). Knutson and Tao proved that another equivalent condition for such A, B and C to exist is that there is a hive (defined within) whose boundary is (log alpha, log beta, log gamma). The logarithms of the coefficients of F approximately form such a hive; this leads to a new proof of Knutson and Tao's result. This paper uses no representation theory and essentially no symplectic geometry. In their place, it uses Viro's patchworking method and a topological description of Vinnikov curves. | |
| dc.identifier | https://arxiv.org/abs/math/0311428 | |
| dc.identifier | http://arxiv.org/abs/math/0311428 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69328 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Representation Theory | |
| dc.title | Horn's Problem, Vinnikov Curves and the Hive Cone | |
| dc.type | text |