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math.AG2026
Analytic Bertini theorem II --- The local case
Mingchen Xia
We prove the local analytic Bertini theorem, confirming a conjecture of Boucksom in full generality.
math.AG2026
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…
math.AG2026
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…