By F. A. Bogomolov, A. N. Landia (auth.), H. Kurke, J. H. M. Steenbrink (eds.)

ISBN-10: 9400906854

ISBN-13: 9789400906853

ISBN-10: 9401067937

ISBN-13: 9789401067935

The convention on Algebraic Geometry, held in Berlin 9-15 March 1988, was once organised by way of the Sektion Mathematik of the Humboldt-Universitat. The setting up committee consisted of H. Kurke, W. Kleinert, G. Pfister and M. Roczen. The convention is one in a chain organised via the Humboldt-Universitat at normal periods of 2 or 3 years, with the aim of delivering a gathering position for mathematicians from jap and western international locations. the current quantity includes gildings of a part of the lectures provided on the convention and a few articles on comparable matters. All papers have been topic to the commonplace refereeing method of Compositio Mathematica, and H. Kurke acted as a visitor editor of this magazine. The papers specialize in real topics in algebraic geometry and singularity idea, resembling vector bundles, arithmetical algebraic geometry, intersection thought, moduli and Hodge thought. we're thankful to all those that, through their hospitality, their presence on the Con ference, their aid or their written contributions, have made this convention to successful. The editors Compositio Mathematica seventy six: viii, 1990.

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**Extra resources for Algebraic Geometry: Proceedings of the Conference at Berlin 9–15 March 1988**

**Sample text**

For varieties over the complex numbers, Z a point and X\Z smooth, the above result for mixed Hodge structures on ordinary cohomology was deduced by several people [Stl, EI] using the characteristic 0 decomposition theorem. Later Steenbrink and Navarro found a more elementary proof using Hodge theory [St2, Na]. 1 follows naturally from the second author's theory of mixed Hodge modules combined with the theory of gluing tstructures from [BBD]. The proof is in the spirit of the second proof of local purity in the l-adic case.

PROPOSITION. AzD u) (iii) IHn+k(L) = Hk«az)*AzIC u) = Hk+ l«a z )*Az IC u) and the same for H~(L), HfM(L) and IH~+k(L) with (az)* and (a z)! exchanged. 10. For the isomorphism (i), let F = Qu. 11].

The above examples are independent of this result, and hence provide new restrictions on the topology of complex algebraic varieties. , ... ) We use no more properties than those summarized in [GM2 Sect. 1]. Various properties of the intersection homology of links are stated and proved in this language. Of course no conclusions can be drawn about weights (Sect. 4) or the resulting corollaries on the topological structure of varieties (Sect. 5). The category of mixed Hodge modules on X: The additional material we need about mixed Hodge modules is basically the same as the formalities of [BBD].

### Algebraic Geometry: Proceedings of the Conference at Berlin 9–15 March 1988 by F. A. Bogomolov, A. N. Landia (auth.), H. Kurke, J. H. M. Steenbrink (eds.)

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