 
Summary: Mathematische Zeitschrift manuscript No.
(will be inserted by the editor)
Alberto Saracco · Giuseppe Tomassini
Cohomology and extension problems for
semi qcoronae
Received: date
Abstract We prove some extension theorems for analytic objects, in particu
lar sections of a coherent sheaf, defined in semi qcoronae of a complex space.
Semi qcoronae are domains whose boundary is the union of a Levi flat part, a q
pseudoconvex part and a qpseudoconcave part. Such results are obtained mainly
using cohomological techniques.
Keywords qpseudoconvexity · cohomology · extension
Mathematics Subject Classification (2000) Primary 32D15 · Secondary
32F10 · 32L10
1 Introduction.
Let X be a (connected and reduced) complex space of dimension n. We recall that
X is said to be strongly qpseudoconvex in the sense of AndreottiGrauert [AG]
(q 1) if there exists a compact subset K and a smooth function : X R,
0, which is strongly qplurisubharmonic1 on X K and such that:
a) 0 = min
