Mixed Hodge-Riemann bilinear relations and m-positivity In Memory of Professor Zhengguo Bai(1916-201

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Motivated by our previous work on Hodge-index type theorems,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(1998)and Dinh and Nguyên(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 K?hler manifolds.
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