8 citations · 36 across the 11 of their papers we have counts for
8 papers · 1 filter
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…
On the positivity of high-degree Schur classes of an ample vector bundle
Jian Xiao
Let be a smooth projective variety of dimension , and let be an ample vector bundle over . We show that any non-zero Schur class of , lying in the cohomology group…
Mixed Hodge-Riemann bilinear relations and -positivity
Jian Xiao
Motivated by our previous work on Hodge-index type inequalities, we give a form of mixed Hodge-Riemann bilinear relation by using the notion of -positivity, whose proof is an ad…
Hodge-index type inequalities, hyperbolic polynomials and complex Hessian equations
Jian Xiao
It is noted that using complex Hessian equations and the concavity inequalities for elementary symmetric polynomials implies a generalized form of Hodge index inequality. Inspired…
Characterizing volume via cone duality
Jian Xiao
For divisors over smooth projective varieties, we show that the volume can be characterized by the duality between pseudo-effective cone of divisors and movable cone of curves. Ins…
Teissier's problem on proportionality of nef and big classes over a compact Kähler manifold
Jixiang Fu, Jian Xiao
We solve Teissier's proportionality problem for transcendental nef classes over a compact Kähler manifold which says that the equality in the Khovanskii-Teissier inequalities hold…