By Kraft
In recent times, there was expanding curiosity and task within the region of crew activities on affine and projective algebraic types. Tech niques from quite a few branches of arithmetic were vital for this research, in particular these coming from the well-developed idea of tender compact transformation teams. It used to be well timed to have an interdisciplinary assembly on those subject matters. We prepared the convention "Topological equipment in Alg~braic Transformation Groups," which was once held at Rutgers collage, 4-8 April, 1988. Our target used to be to facilitate an trade of principles and strategies between mathematicians learning compact tender transformation teams, alge braic transformation teams and similar concerns in algebraic and analytic geometry. The assembly used to be good attended, and those court cases provide a bigger viewers the chance to profit from the wonderful survey and really good talks provided. the most themes involved a number of as pects of staff activities, algebraic quotients, homogeneous areas and their compactifications. The assembly was once made attainable through aid from Rutgers college and the nationwide technology starting place. We convey our deep appreciation for this aid. We additionally thank Annette Neuen for her suggestions with the technical guidance of those complaints.
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Example text
This paper deals with the Fixed Point Problem (see [PRl]). Does an algebraic action of a reductive group on affine space Fn have a fixed point? In order to treat this problem there are two obvious properties of the situation which might be crucial: (1) The homological property that Fn is acyclic. , the group is finite). Do these properties individually or jointly imply the existence of a fixed point? Certainly they playa role. For example, any cyclic group G not of prime power order acts smoothly on R n without fixed points, where n depends on G (see [B, pp.
In section 3 we illustrate the use of Cremona transformations in showing that homology planes have tidy plane divisors. As mentioned, these techniques have been used to convert complicated plane divisors into linear plane divisors and hopefully will play a role in answering the question of whether every homology plane has a linear plane divisor. Acknowledgement. This seems to be a good point to acknowledge the week of stimulating conversations the second author of this paper had at the University of Osaka with Miyanishi a few months prior to the Rutgers Conference.
Math. 84 (1986), 617-632. [BP] M. Brion, F. Pauer, Valuations des espaces homogenes spheriques, Comment. Math. Helv. 62 (1987),265-285. [DR1] J. J. Duistermaat, G. Heckman, On the variation in the cohomology of the symplectic form of the reduced phase space, Invent. math. 69 (1982), 259-268. [DR2] J. J. Duistermaat, G. Heckman, Addendum to "On the variation ... ", Invent. math. 72 (1983), 153-158. [DP1] C. DeConcini, C. Procesi, Complete symmetric varieties, Invariant theory, Springer Lecture Notes 996.
