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 by way of 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 sequence organised via the Humboldt-Universitat at standard durations of 2 or 3 years, with the aim of delivering a gathering position for mathematicians from jap and western nations. the current quantity includes embellishments of a part of the lectures awarded on the convention and a few articles on similar 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 concentrate on real topics in algebraic geometry and singularity conception, equivalent to vector bundles, arithmetical algebraic geometry, intersection concept, moduli and Hodge conception. we're thankful to all those that, via 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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W = (y - 1 )* W And there is character Xy: G -+ IC* such that y. g = Xy(y)g for any y E G. In this situation we call (Y, 0) a G-singularity. Note that this setting is larger than in Wall [27] where one takes Xy = 1, but coincides (in the case of G cyclic) to the hyperquotient singularity notion of M. Reid [19]. o, d) be the subcomplex in (n~,o, d) consisting of the fixed elements under the obvious action of G. If K· is any complex of IC-vector spaces with G-actions compatible with the differentials, then there is a natural isomorphism H·(K· G) = H·(K·)G which says that taking cohomology commutes with taking the fixed parts under G.

IHES 40, 5-58 (1971) and 44, (1974) 5 -77. 6. A. Dimca, On the homology and cohomology of complete intersections with isolated singularities. Compositio Math. 58, (1986) 321-339. 7. A. Dimca, Topics on Real and Complex Singularities, Braunschweig-Wiesbaden: Vieweg 1987. 8. I. Dolgachev, Weighted projective varieties. B. (ed) Group Actions and Vector Fields, Proceedings 1981. (Lect. , vol. 956, pp. 34-71) Berlin Heidelberg New York: Springer 1982. 9. H. Esnault, Fibre de Milnor d'un cone sur une courbe plane singuliere, Invent.

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. (The stratification of d- 1(e) is induced by a complex Whitney stratification of X compatible with Z).