Hodge-index type inequalities, hyperbolic polynomials and complex Hessian equations
Algebraic Geometry
2018-10-11 v1 Complex Variables
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 . 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.
Cite
@article{arxiv.1810.04662,
title = {Hodge-index type inequalities, hyperbolic polynomials and complex Hessian equations},
author = {Jian Xiao},
journal= {arXiv preprint arXiv:1810.04662},
year = {2018}
}