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- W2888460730 abstract "In this article, we study the structure of the cone of semidefinite forms. It is a closed semialgebraic set but usually is not basic closed semialgebraic set. A discriminant is a defining equation of an irreducible component of algebraic boundary of this cone. We calculate discriminants using new tools – characteristic variety and local cones. A characteristic variety is a semialgebraic subset of a real projective variety on which the family of inequalities is essentially defined as linear functions. Local cone is a subcone of the PSD cone which corresponds to a maximal ideal. This theory works well for a family of polynomials which are invariant under an action of a finite group. After we construct an abstract general theory, we apply it to a family of cyclic homogeneous polynomials of three real variables of degree d . We calculate some discriminants for d = 3 , 4, 5 and 6, and we show that this theory derives many new results." @default.
- W2888460730 created "2018-08-31" @default.
- W2888460730 creator A5049201390 @default.
- W2888460730 date "2018-11-01" @default.
- W2888460730 modified "2023-09-29" @default.
- W2888460730 title "Discriminants of cyclic homogeneous inequalities of three variables" @default.
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- W2888460730 doi "https://doi.org/10.1016/j.jalgebra.2018.07.036" @default.
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