14 citations · 41 across the 16 of their papers we have counts for
6 papers · 1 filter
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…
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…