From the 1 of 5 linked papers with an AI index.
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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…
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…
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 bo…