Summary: Mathematische Zeitschrift manuscript No.
(will be inserted by the editor)
Alberto Saracco · Giuseppe Tomassini
Cohomology and extension problems for
Abstract We prove some extension theorems for analytic objects, in particu-
lar sections of a coherent sheaf, defined in semi q-coronae of a complex space.
Semi q-coronae are domains whose boundary is the union of a Levi flat part, a q-
pseudoconvex part and a q-pseudoconcave part. Such results are obtained mainly
using cohomological techniques.
Keywords q-pseudoconvexity · cohomology · extension
Mathematics Subject Classification (2000) Primary 32D15 · Secondary
32F10 · 32L10
Let X be a (connected and reduced) complex space of dimension n. We recall that
X is said to be strongly q-pseudoconvex in the sense of Andreotti-Grauert [AG]
(q 1) if there exists a compact subset K and a smooth function : X R,
0, which is strongly q-plurisubharmonic1 on X K and such that:
a) 0 = min