14 citations · 41 across the 16 of their papers we have counts for
16 papers
A counterexample to the zero-mass conjecture
Long Li, Mingchen Xia
We construct an explicit negative plurisubharmonic function on the unit polydisk in with an isolated singularity at the origin. Its Monge-Ampère measure is…
Analytic Bertini theorem II --- The local case
Mingchen Xia
We prove the local analytic Bertini theorem, confirming a conjecture of Boucksom in full generality.
Transcendental b-divisors II -- Monotonicity theorem
Mingchen Xia
In this paper, we develop the general intersection theory of nef b-divisors, extending the movable intersection theory. We define a notion of restricted volume of b-divisors and pr…
Transcendental b-divisors I -- Correspondence with currents
Mingchen Xia
We study transcendental b-divisors over compact Kähler manifolds. We establish the correspondence between closed positive currents and nef b-divisors. As an application, we establi…
A transcendental approach to non-Archimedean metrics of pseudoeffective classes
Tamás Darvas, Mingchen Xia, Kewei Zhang
We introduce the concept of non-Archimedean metrics attached to a transcendental pseudoeffective cohomology class on a compact Kähler manifold. This is obtained via extending the R…
Non-pluripolar products on vector bundles and Chern--Weil formulae
Mingchen Xia
In this paper, we develop several pluripotential-theoretic techniques for singular metrics on vector bundles. We first introduce the theory of non-pluripolar products on holomorphi…
Partial Okounkov bodies and Duistermaat--Heckman measures of non-Archimedean metrics
Mingchen Xia
Let be a smooth projective variety. We construct partial Okounkov bodies associated to Hermitian pseudo-effective line bundles on . We show that partial Okounkov bod…
The volume of pseudoeffective line bundles and partial equilibrium
Tamás Darvas, Mingchen Xia
Let be a pseudoeffective line bundle on an -dimensional compact Kähler manifold . Let be the dimension of the space of sectio…
Analytic Bertini theorem
Mingchen Xia
We prove an analytic Bertini theorem, generalizing a previous result of Fujino and Matsumura.
On Liu morphisms in non-Archimedean geometry
Mingchen Xia
We define Liu morphisms and quasi-Liu morphisms between Berkovich analytic spaces. We show that Liu morphisms and quasi-Liu morphisms behave exactly as affine morphisms and quasi-a…
Pluripotential-theoretic stability thresholds
Mingchen Xia
Given a compact polarized manifold , we introduce two new stability thresholds in terms of singularity types of global quasi-plurisubharmonic functions on . We prove that…
The closures of test configurations and algebraic singularity types
Tamás Darvas, Mingchen Xia
Given a Kähler manifold with an ample line bundle , we consider the metric space of geodesic rays associated to the first Chern class . We characterize rays th…
Integration by parts formula for non-pluripolar product
Mingchen Xia
In this paper, we prove the integration by parts formula for the non-pluripolar product on a compact Kähler manifold. Our result generalizes the special case of potentials with sma…
Mabuchi geometry of big cohomology classes with prescribed singularities
Mingchen Xia
Let be a compact Kähler unibranch complex analytic space of pure dimension. Fix a big class with smooth representative and a model potential with positive mass. We…
On sharp lower bounds for Calabi type functionals and destabilizing properties of gradient flows
Mingchen Xia
Let be a compact Kähler manifold with a given ample line bundle . In \cite{Don05}, Donaldson proved that the Calabi energy of a Kähler metric in is bounded from bel…
Deligne-Riemann-Roch Theorems I. Uniqueness of Deligne Pairings and Degree Part of Deligne-Riemann-Roch Isomorphisms
Mingchen Xia
This is the first of a series of papers. Our final goal is to establish Deligne-Riemann-Roch isomorphisms in various settings. In this paper, we establish a uniqueness theorem for…