2006/03/23 by Taras Panov, Panov, Taras · 1 citation
Mathematics · #14L30 #14M25 #57S25 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.AG #math.AT #msc:14L30 #msc:14M25 #msc:57S25
paper · pdf · doi:10.48550/arxiv.math/0603556
15 pages, LaTeX2e; minor corrections
openalex publication_date 2006/03/23 · arxiv created 2008/10/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the theory of algebraic group actions on affine varieties, the concept of a Kempf-Ness set is used to replace the categorical quotient by the quotient with respect to a maximal compact subgroup. By making use of the recent achievements of "toric topology" we show that an appropriate notion of a Kempf-Ness set exists for a class of algebraic torus actions on quasiaffine varieties (coordinate subspace arrangement complements) arising in the Batyrev-Cox "geometric invariant theory" approach to toric varieties. We proceed by studying the cohomology of these "toric" Kempf-Ness sets. In the case of projective non-singular toric varieties the Kempf-Ness sets can be described as complete intersections of real quadrics in a complex space.