3 citations · 4 across the 6 of their papers we have counts for
6 papers
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-Se…
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 whi…
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…
Hard Lefschetz theorems for free line bundles
Jiajun Hu, Shijie Shang, Jian Xiao
We introduce a partial positivity notion for algebraic maps via the defect of semismallness. This positivity notion is modeled on -positivity in the analytic setting and -amp…
Intersection theoretic inequalities via Lorentzian polynomials
Jiajun Hu, Jian Xiao
We explore the applications of Lorentzian polynomials to the fields of algebraic geometry, analytic geometry and convex geometry. In particular, we establish a series of intersecti…
Hard Lefschetz properties, complete intersections and numerical dimensions
Jiajun Hu, Jian Xiao
We study the positivity of complete intersections of nef classes. We first give a sufficient and necessary characterization on the complete intersection classes which have hard Lef…