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Multiple discriminants and critical values of a multivariate polynomial

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arxiv 1508.00551 v1 pith:FXRLHN7M submitted 2015-08-03 math.AC

Ruslan Sharipov This is my paper · ORCID
classification math.AC
keywords criticalfunctionvaluecaseequationmultivariatepolynomialvalues
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A critical value of a function is the value of this function at one of its critical points. Each critical point of a differentiable multivariate function is described by the equations which consist in equating to zero all of its partial derivatives. However, in general case there is no equation for the corresponding critical value. The case of polynomials is different. In the present paper an equation for critical values of a polynomial is derived.

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  1. Algebraic conditions for the positivity of sectional curvature

    math.DG 2019-08 conditional novelty 5.0 of 10

    For n=4, the real roots of the y-discriminant of det(R-xI-yK) locate the critical values of sectional curvature, exactly on the dense open set where the discriminant of that polynomial is nonzero.

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