no code implementations • 4 Feb 2021 • Junyan Cao, Henri Guenancia, Mihai Păun
In this note, we obtain various formulas for the curvature of the $L^2$ metric on the direct image of the relative canonical bundle twisted by a holomorphic line bundle endowed with a positively curved metric with analytic singularities, generalizing some of Berndtsson's seminal results in the smooth case.
Complex Variables Algebraic Geometry
no code implementations • 3 Dec 2020 • Vincent Guedj, Henri Guenancia, Ahmed Zeriahi
In this note, we investigate some regularity aspects for solutions of degenerate complex Monge-Amp\`ere equations (DCMAE) on singular spaces.
Complex Variables Differential Geometry
no code implementations • 1 Dec 2020 • Benjamin Bakker, Henri Guenancia, Christian Lehn
We extend the decomposition theorem for numerically $K$-trivial varieties with log terminal singularities to the K\"ahler setting.
Algebraic Geometry Complex Variables 32Q25, 32J27 (Primary), 32S15, 32Q20 (Secondary)
