Cohomology and removable subsets

TL;DR

This paper generalizes cohomology finiteness and vanishing theorems for complex spaces with specific boundary structures, leading to new results on extension problems and removable sets for sheaves and analytic subsets.

Contribution

It extends previous cohomology theorems to complex spaces with q-collars, providing new insights into extension and removability of analytic objects.

Findings

Generalized cohomology finiteness and vanishing theorems for q-collars.

Established extension results for sections of coherent sheaves.

Identified conditions for removability of analytic subsets.

Abstract

Let X be a (connected and reduced) complex space. A q-collar of X is a bounded domain whose boundary is a union of a strongly q-pseudoconvex, a strongly q-pseudoncave and two flat (i.e. locally zero sets of pluriharmonic functions) hypersurfaces. Finiteness and vanishing cohomology theorems obtained in math/0503490 and math/0701549 for semi q-coronae are generalized in this context and lead to results on extension problem and removable sets for sections of coherent sheaves and analytic subsets.