Jian Xiao

activity

20152020

most citedCharacterizing volume via cone duality

6 citations · 9 across the 3 of their papers we have counts for

collaborators

5 papers

math.AG2020★ 3 cited

On the positivity of high-degree Schur classes of an ample vector bundle

Jian Xiao

Let $X$ be a smooth projective variety of dimension $n$ , and let $E$ be an ample vector bundle over $X$ . We show that any non-zero Schur class of $E$ , lying in the cohomology group…

math.AG2018

Mixed Hodge-Riemann bilinear relations and $m$ -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 $m$ -positivity, whose proof is an ad…

math.AG2018

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…

math.DG2015

A remark on the convergence of inverse $σ_{k}$ -flow

Jian Xiao

We study the positivity of related cohomology classes concerning the convergence problem of inverse $σ_{k}$ -flow in the conjecture proposed by Lejmi and Székelyhidi.

math.AG2015★ 6 cited

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…

On the positivity of high-degree Schur classes of an ample vector bundle

Mixed Hodge-Riemann bilinear relations and m-positivity

Hodge-index type inequalities, hyperbolic polynomials and complex Hessian equations

A remark on the convergence of inverse σk​-flow

Characterizing volume via cone duality

Mixed Hodge-Riemann bilinear relations and $m$ -positivity

A remark on the convergence of inverse $σ_{k}$ -flow