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 through 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 by way of the Humboldt-Universitat at general durations of 2 or 3 years, with the aim of delivering a gathering position for mathematicians from japanese and western nations. the current quantity comprises embellishments of a part of the lectures provided on the convention and a few articles on comparable matters. All papers have been topic to the usual refereeing process of Compositio Mathematica, and H. Kurke acted as a visitor editor of this magazine. The papers specialise in genuine topics in algebraic geometry and singularity idea, comparable to vector bundles, arithmetical algebraic geometry, intersection concept, moduli and Hodge thought. we're thankful to all those that, by means of their hospitality, their presence on the Con ference, their aid or their written contributions, have made this convention to a hit. The editors Compositio Mathematica seventy six: viii, 1990.

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15, (1974) 1061-1082. Compositio Mathematica 76: 49-67, 1990. © 1990 Kluwer Academic Publishers. Mixed Hodge structures on the intersection cohomology of links ALAN H. DURFEE 1 * & MORIHIKO SAIT0 2 ** 1 Mount Holyoke College, South Hadley, MA USA-01075; 2 RIMS Kyoto University, Kyoto 606 Japan Received 4 November 1988; accepted in revised form 16 March 1990 Keywords: Mixed Hodge structures, links of singularities, intersection homology, mixed Hodge modules, semipurity, topology of algebraic varieties.

5, then in Db(Z) there is a natural functorial isomorphism Proof Let rf be the restriction of r to N*. We have natural morphisms of r~F to i*j*F and r*k* F, and since r is proper it is easy to check that they are quasiisomorphisms. 10. PROPOSITION. Qu ® k* F -4 kiF gives a natural isomorphism k* F [ - 1] = k! F. So by duality it is enough to show the first isomorphism. 2(i), H·d~F is constant on (0,1), and the natural morphisms are quasi-isomorphisms. 9. 11. 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)!

When all the singularities ga are weighted homogeneous, it is enough to take m ~ n + 1. Proof On a formal level, note that the formulas in (i) are a special case of the formulas in (ii), obtained by taking m divisible by all ka = 1Gal, a E Z. The proof of (i) is purely topological and independent of our previous results. Let a, H, ... , be as above. We may takef' close enough to f such that for all aE Z the intersection Fa = B. n (I'

### 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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