Mixed Hodge-Riemann bilinear relations andm-positivity

Motivated by our previous work on Hodge-index type theorems, we give a form of mixed Hodge-Riemann bilinear relation by using the notion ofm-positivity, whose proof is an adaptation of the works of Timorin (1998) and Dinh and Nguyen (2006). 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 Kahler manifolds.

Automated summary

Inspired by previous work on Hodge-index type theorems, this study presents a mixed Hodge-Riemann bilinear relation using the notion of m-positivity. The proof is an adaptation of previous works and it holds with respect to mixed polarizations, some of which satisfy particular positivity conditions but may be degenerate along certain directions. This relation is particularly applicable to fibrations of compact Kahler manifolds.