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math.AG2023
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.AG2023
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…
math.AG2023★ 3 cited
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…