Every closed positive (1,1)-current can be approximated by currents with analytic singularities - this result uses in an essential way the Ohsawa-Takegoshi L2 extension theorem in its proof, and can be seen as a generalization of Zariski decomposition in algebraic geometry. We use these techniques to derive several consequences in algebraic and analytic geometry :
- an optimal lower bound for the log canonical threshold of isolated plurisubharmonic singularities (joint work with Pham Hoang Hiep)
- results on asymptotic cohomology, in relation with holomorphic Morse inequalities and an inverse Andreotti-Grauert theorem.
- regularity theorems for solutions of Monge-Ampère equations.