Hodge filtration on local cohomology and applications
HARVARD-MIT ALGEBRAIC GEOMETRY
Mihnea Popa - Harvard University
This describes joint work in progress with M. Mustata, in which we study the filtration on local cohomology sheaves induced by their natural mixed Hodge module structure. Special properties of this filtration, for instance strictness, lead to a number of different applications, including an injectivity theorem for dualizing complexes, local vanishing for forms with log poles, and especially a characterization of the local cohomological dimension of a closed subscheme in terms of data arising from a log resolution of singularities.