1999/11/22 by Miles Reid, Reid, Miles · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG
paper · pdf · doi:10.48550/arxiv.math/9911165
20 pages, uses Latex and bourbaki.cls. Séminaire Bourbaki, 52ème année, novembre 1999, no. 867, to appear in Astérisque 2000
arxiv created 1999/11/22 · openalex publication_date 1999/11/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a quasiprojective algebraic manifold with KM=0 and G a finite automorphism group of M acting trivially on the canonical class KM; for example, a subgroup G of SL(n,C) acting on Cn in the obvious way. We aim to study the quotient variety X=M/G and its resolutions Y -> X (especially under the assumption that Y has KY=0) in terms of G-equivariant geometry of M. At present we know 4 or 5 quite different methods of doing this, taken from string theory, algebraic geometry, motives, moduli, derived categories, etc. For G in SL(n,C) with n=2 or 3, we obtain several methods of cobbling together a basis of the homology of Y consisting of algebraic cycles in one-to-one correspondence with the conjugacy classes or the irreducible representations of G.