Cohomology and removable subsets

2008/02/01 by Alberto Saracco, Saracco, Alberto, Giuseppe Tomassini +1
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #msc:32C25 #msc:32D15 #msc:32D20 #msc:32F10

paper · pdf · doi:10.48550/arxiv.0802.0159

17 pages, 2 figures

arxiv created 2008/02/01 · arxiv updated 2009/12/01

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.

Related

• Cohomology and extension problems for semi q-coronae
• The ∂-problem on Z(q)-domains
• Strong q-convexity in uniform neighborhoods of subvarieties in coverings of complex spaces
• On q-complete and q-concave with corners complex manifolds
• On rigid q-plurisubharmonic functions and q-pseudoconvex tube domains in ℂⁿ