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math.CV2026
Big and nef cohomology classes on compact Kähler spaces
Duc-Viet Vu
We first prove a version of the Demailly-Paun theorem for compact weakly Kaehler spaces. Secondly, for a big and nef Bott-Chern class on a compact normal Kaehler space, we prove th…
math.CV2026
Positivity of Smooth Currents on Singular Spaces
Duc-Thai Do, Duc-Viet Vu
We study two notions of positivity for smooth currents on singular spaces. We show that they are not equivalent by establishing a necessary condition on the fourth Whitney cones. W…
math.CV2026
Quantitative hyperbolicity for complex manifolds via numerical invariants
Tien-Cuong Dinh, Duc-Bao Nguyen, Duc-Viet Vu
We introduce numerical invariants called hyperbolic indices, which measure the hyperbolicity of compact Kähler manifolds using directed positive closed currents. We prove that if a…