By Wolf Barth (auth.), Ingrid Bauer, Fabrizio Catanese, Thomas Peternell, Yujiro Kawamata, Yum-Tong Siu (eds.)

ISBN-10: 3642562027

ISBN-13: 9783642562020

ISBN-10: 3642627900

ISBN-13: 9783642627903

This quantity includes a selection of study papers devoted to Hans Grauert at the social gathering of his 70th birthday. Hans Grauert is a pioneer in smooth advanced research, carrying on with the il lustrious German culture in functionality idea of numerous complicated variables of Weierstrass, Behnke, Thullen, Stein, Siegel, etc. while Grauert got here at the scene within the early 1950's, functionality conception used to be dealing with a innovative interval with the geometric thought of advanced areas nonetheless in its embryonic degree. A wealthy conception advanced with the joint efforts of many nice mathematicians together with Oka, Kodaira, Cartan, and Serre. the automobile tan Seminar in Paris and the Kodaira Seminar supplied very important venues an for its improvement. Grauert, including Andreotti and Remmert, took energetic half within the latter. In his occupation he has nurtured various his personal doctoral scholars in addition to different younger mathematicians in his box from allover the area. For a few a long time his paintings blazed the path and set the examine time table in different complicated variables all over the world. between his many essentially very important contributions, that are too quite a few to totally enumerate right here, are: 1. the full explanation of varied notions of complicated areas. 2. the answer of the overall Levi challenge and his paintings on pseudo convexity for basic manifolds. three. the idea of outstanding analytic units. four. The Oka precept for holomorphic bundles. five. The facts of the Mordell conjecture for functionality fields. 6. The direct photograph theorem for coherent sheaves.

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The quartic Y containing the additional line L C Q then will split off Q. Hence Y will be one of the four pairs of quadrics in the linear system different from Ql +Q2' 0 L~ 00 5 • , 00 • , Double Quadrics with Eight Nodes A double quadric is a K3-surface Y, birational to a double cover a' : Y' -t of a quadric. This is branched over a curve S C IP'I X IP'I of type IP'I X IP'I 22 W. Barth (4,4). Here we assume that 8 is smooth but for eight nodes s1, ... , Ss E 8. They correspond to eight nodes el, ...

32 Th. Bauer et al. 6. Let a be a nef cohomology class on a smooth projective variety X. Then there exists an almost holomorphic, dominant rational map f : X --+ Y with connected fibers, such that 1. a is numerically trivial on all compact fibers F of f with dim F = dim X dimY 2. for every general point x E X and every irreducible curve C passing through x with dimf{C) > 0, we have a· C > O. The map f is unique up to birational equivalence of Y. In particular, if two general points of X can be joined by a chain C of curves such that a· C = 0, then a == O.

Demailly, Vanishing theorems and effective results in algebraic geometry, Trieste lecture notes, 2000. [Ha70] R. Hartshorne, Ample subvarieties of algebraic varieties, Lecture Notes in Mathematics 156 (1970), Springer. [HL83] R. B. Lawson, An intrinsic characterization of Kahler manifolds, Invent. Math. 74 (1983), 169-198. [Pa98] M. Paun, Sur l'effectivite numerique des images inverses de fibres en droites, Math. Ann. 310 (1998), 411-42l. [TsOO] H. AG/000l023, October 2000. Canonical Rings of Surfaces Whose Canonical System has Base Points Ingrid C.

### Complex Geometry: Collection of Papers Dedicated to Hans Grauert by Wolf Barth (auth.), Ingrid Bauer, Fabrizio Catanese, Thomas Peternell, Yujiro Kawamata, Yum-Tong Siu (eds.)

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