February 22, 2017

Algebraic Geometry: Proceedings of the Conference at Berlin by F. A. Bogomolov, A. N. Landia (auth.), H. Kurke, J. H. M.

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

The convention on Algebraic Geometry, held in Berlin 9-15 March 1988, used to be organised through the Sektion Mathematik of the Humboldt-Universitat. The establishing 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 common periods of 2 or 3 years, with the aim of supplying a gathering position for mathematicians from japanese and western international locations. the current quantity includes embellishments of a part of the lectures awarded on the convention and a few articles on similar topics. All papers have been topic to the commonplace refereeing technique of Compositio Mathematica, and H. Kurke acted as a visitor editor of this magazine. The papers concentrate on real topics in algebraic geometry and singularity conception, reminiscent of vector bundles, arithmetical algebraic geometry, intersection concept, moduli and Hodge conception. we're thankful to all those that, through their hospitality, their presence on the Con­ ference, their help or their written contributions, have made this convention to a hit. The editors Compositio Mathematica seventy six: viii, 1990.

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Ii) For any F in D~(N*) such that HiF is locally constant on each stratum of N*, the natural morphisms afd*j*F)o --+ H"(Z, i*j*F) are isomorphisms. Note that condition (ii) is always satisfied if d is proper. 3. Suppose Z is compact. A stratified topological pseudomanifold L is an analytic link of Z in X, if there exists a nonnegative real analytic distance function d: N --+ [0,1) where N is an open neighborhood of Z in X, such that Z = d- 1(0) and L is isomorphic to d- 1(e) as stratified space (up to a refinement of stratification) for < E « 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]. This material is summarized in the first section of this paper. The category of mixed l-adic sheaves on a variety in characteristic p: Lastly, this paper can be read in the setting of [BBD], with the conclusions of Sect.

H~(W): The kth cohomology group, resp. cohomology group with compact supports. Hk(W), resp. HfM(W): The kth homology group, resp. Borel-Moore ho- mology group (homology with closed supports). IHdW), resp. IHfM(W): The kth intersection homology group with middle perversity k-dimensional chains with compact support, resp. 2; Bo l]. Since W has even codimensional strata, the middle perversity is well defined. IHk(W), resp. ~k(W), resp. cohomology with compact supports, defined as IHm-k(W). 2. 3. Let X be a complex algebraic variety (a reduced separated scheme of finite type over C), assumed irreducible and of complex dimension n.

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