Andreotti-Grauert theory by integral formulas. (Licensed ed. of the Akademie Verlag, Berlin). (English) Zbl 0654.32002

Henkin, Gennadi M.; Leiterer, Jürgen

Progress in Mathematics, 74. Basel etc.: Birkhäuser Verlag. 270 P. (1988).

MSC:

32-02	Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces
32A25	Integral representations; canonical kernels (Szegő, Bergman, etc.)
32F10	\(q\)-convexity, \(q\)-concavity
32W05	\(\overline\partial\) and \(\overline\partial\)-Neumann operators

Keywords:

Andreotti-Grauert theory; cohomology of q-convex and q-concave manifolds; explicith member of M as explicitly as possible (\({\mathcal M}\) is a quotient of a homogeneous manifold by a discrete group, but the action may be bad and \({\mathcal M}\) may have no analytic structure). The author studies and classifies also rational endomorphism rings of T. The pair (T,G) is called special if the complex representation factors through \(SL_ 2({\mathbb{C}})\). Such pairs are studied more in detail. The lattice structure of \(H^ 2(T; {\mathbb{Z}})\) is studied and several interesting relations are given. For example, a necessary and sufficient condition for a singular abelian surface T to admit a special action of a given group G is given in terms of the Neron-Severi lattice of T