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Mathematische Zeitschrift manuscript No. (will be inserted by the editor)

Summary: Mathematische Zeitschrift manuscript No.
(will be inserted by the editor)
Alberto Saracco Giuseppe Tomassini
Cohomology and extension problems for
semi q-coronae
Received: date
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
1 Introduction.
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


Source: Abbondandolo, Alberto - Scuola Normale Superiore of Pisa


Collections: Mathematics