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- W4306804769 abstract "The Gram spectrahedron of a real form $finmathbb{R}[underline{x}]_{2d}$ parametrizes all sum of squares representations of $f$. It is a compact, convex, semi-algebraic set, and we study its facial structure in the case of ternary quartics, i.e. $finmathbb{R}[x,y,z]_4$. We show that the Gram spectrahedron of every smooth ternary quartic has faces of dimension 2, and generically none of dimension 1. We complete the proof that the so called Steiner graph of every smooth quartic is isomorphic to $K_4coprod K_4$. Moreover, we show that the Gram spectrahedron of a generic psd ternary quartic contains points of all ranks in the Pataki interval." @default.
- W4306804769 created "2022-10-20" @default.
- W4306804769 creator A5053821982 @default.
- W4306804769 date "2023-05-01" @default.
- W4306804769 modified "2023-10-17" @default.
- W4306804769 title "Gram spectrahedra of ternary quartics" @default.
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- W4306804769 doi "https://doi.org/10.1016/j.jsc.2022.10.004" @default.
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