Mixed Hodge-Riemann bilinear relations and m-positivity

2018/11/14 by Xiao, Jian · 1 citation
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.05865

Abstract

Motivated by our previous work on Hodge-index type inequalities, we give a form of mixed Hodge-Riemann bilinear relation by using the notion of m-positivity, whose proof is an adaptation of the works of Timorin and Dinh-Nguyên. This mixed Hodge-Riemann bilinear relation holds with respect to mixed polarizations in which some satisfy particular positivity condition, but could be degenerate along some directions. In particular, it applies to fibrations of compact Kähler manifolds.

Cited by

• Lefschetz theorems, Hodge-Riemann relations and Ample vector bundles

Related

• Hodge-index type inequalities, hyperbolic polynomials and complex Hessian equations
• The mixed Hodge-Riemann bilinear relations for compact Kahler manifolds
• Variations of mixed Hodge structure and semi-positivity theorems
• Positivity for Hodge modules and geometric applications
• Positivity of vector bundles and Hodge theory