3 papers
math.AG2026
Numerical characterization of the hard Lefschetz classes of dimension two, I: supercritical collections under certain rearrangement
Jiajun Hu, Jian Xiao
We study the numerical characterization of two dimensional hard Lefschetz classes given by the complete intersections of nef classes. In Shenfeld and van Handel's breakthrough work…
math.AG2025
Numerical characterization of the hard Lefschetz classes of dimension two, II: supercritical collections of free divisor classes
Jiajun Hu, Jian Xiao
For free divisor classes on a smooth projective variety of dimension , the product of these free divisor classes induces a Lefschetz type operator acting on the Néron-S…
math.AG2025
Positivity in the shadow of Hodge index theorem
Jiajun Hu, Jian Xiao
Taking a compact Kähler manifold as playground, we explore the powerfulness of Hodge index theorem. A main object is the Lorentzian classes on a compact Kähler manifold, behind w…