The modified openness conjecture for plurisubharmonic functions

From papers

Let α\alpha and β\beta be plurisubharmonic functions on a complex manifold. Let J(α)\mathcal{J}(\alpha) denote the multiplier ideal sheaf of α\alpha, and let J+(α,β)\mathcal{J}_+(\alpha,\beta) be the maximal element, as t0+t\to0^+, of

{J(α+tβ)t>0}.\{\mathcal{J}(\alpha+t\beta)\mid t>0\}.

Modified openness conjecture. Then

J+(α,β)=J(α).\mathcal{J}_+(\alpha,\beta)=\mathcal{J}(\alpha).

This is a sheaf-theoretic formulation of the openness phenomenon for multiplier ideals and is stated in the paper as a conjectural assertion; no resolution is supplied in the source.

Progress summary

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Sources & referencesView supporting material

Primary source

Dano Kim, “The exactness of a general Skoda complex”, arXiv:1007.0551 (2014).

Solutions 0

No solutions have been posted yet.