2018/10/10 by Xiao, Jian
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.1810.04662
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 Gårding'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.