Resumen de Positive polynomials and hyperdeterminants

Fernando Cukierman

• Let F be a homogeneous real polynomial of even degree in any number of variables.

  We consider the problem of giving explicit conditions on the coefficients so that F is positive definite or positive semidefinite.

  In this note we produce a necessary condition for positivity, and a sufficient condition for nonnegativity, in terms of positivity or semipositivity of a onevariable characteristic polynomial of F. Also, we revisit the known sufficient condition in terms of Hankel matrices.