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Stack structures on GIT quotients parametrizing hypersurfaces

2009/02/25 by Martin G. Gulbrandsen
Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Binary number #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Quotient #Scheme (mathematics) #Stack (abstract data type) #math.AG #msc:14A20 #msc:14L24 #msc:14L30

paper · pdf · doi:10.1002/mana.200810125

published in Mathematische Nachrichten 284(7), 885-898 (Wiley) · 16 pages, 2 figures, to appear in Mathematische Nachrichten

arxiv created 2009/02/25 · openalex publication_date 2011/04/13 · arxiv updated 2011/04/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We suggest to endow Mumford's GIT quotient scheme with a stack structure, by replacing Proj(−) of the invariant ring with its stack theoretic analogue. We analyse the stacks resulting in this way from classically studied invariant rings, and in particular for binary forms of low degree. Our viewpoint is that the stack structure carries interesting geometric information that is intrinsically present in the invariant ring, but lost when passing to its Proj(−). © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Citations