Hodge-index type inequalities, hyperbolic polynomials and complex Hessian equations
Abstract
It is noted that using complex Hessian equations and the concavity inequalities for elementary symmetric polynomials implies a generalized form of Hodge index inequality. Inspired by this result, using Grding's theory for hyperbolic polynomials, we obtain a mixed Hodge-index type theorem for classes of type (1,1). The new feature is that this Hodge-index type theorem holds with respect to mixed polarizations in which some satisfy particular positivity condition, but could be degenerate and even negative along some directions.
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