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arXiv · 1810.04662

Hodge-index type inequalities, hyperbolic polynomials and complex Hessian equations

Jian Xiao
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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 G{\aa}rding'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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Jian Xiao. 2018-10-10. Hodge-index type inequalities, hyperbolic polynomials and complex Hessian equations. https://arxiv.org/abs/1810.04662

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