5 papers
A counterexample to the zero-mass conjecture
Long Li, Mingchen Xia
The authors construct an explicit negative plurisubharmonic function on the unit polydisk whose Monge‑Ampère measure is a Dirac mass at the origin while its Lelong number is zero,…
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 establ…
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…