4 problems

Local smoothing conjecture for holomorphic sections and c9-trace positivity
Let $E$ be a holomorphic vector bundle with a singular Hermitian metric $h$ , and let $c9$ be the Kähler metric from Proposition cref{smoothing of tr-c9 semi-posi for constant secti…
openFrom paperscomplex-geometry positivity singular-hermitian-metrics
0 responses
8
Coherence conjecture for multiplier ideal sheaves of Griffiths semi-positive metrics
Coherence conjecture. If $h$ is Griffiths semi-positive, then $\mathcal{E}(h)$ is coherent.
openFrom paperscomplex-geometry multiplier-ideal-sheaves singular-hermitian-metrics
0 responses
8
Extension theorem without the deformable pseudoeffectivity hypothesis
Let $X$ be a compact Kähler manifold, let $H\to X$ be a holomorphic line bundle, and let $Z\subset X$ be a smooth hypersurface. Let $h$ be a singular Hermitian metric on $H$ satisf…
openFrom paperscomplex-analysis l2-extension singular-hermitian-metrics
0 responses
8
The conjecture on asymptotic expansion of Bergman kernels
Bergman-kernel asymptotics conjecture. The upper and lower local volumes coincide:
openFrom papersbergman-kernels complex-geometry singular-hermitian-metrics
0 responses
12

Local smoothing conjecture for holomorphic sections and c9-trace positivity