2000/03/29 by Annette A’Campo–Neuen, Annette A'Campo-Neuen, A'Campo-Neuen, Annette
Mathematics · #14D25 #14L30 #14M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG #msc:14D25 #msc:14L30 #msc:14M25
paper · pdf · doi:10.48550/arxiv.math/0003204
23 pages, 9 figures, amslateX + pstex; this revised version has a new title and an improved introduction; several typos are corrected
openalex publication_date 2000/03/29 · arxiv created 2004/02/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider subtorus actions on complex toric varieties. A natural candidate for a categorical quotient of such an action is the so-called toric quotient, a universal object constructed in the toric category. We prove that if the toric quotient is weakly proper and if in addition the quotient variety is of expected dimension then the toric quotient is in fact a categorical quotient in the category of algebraic varieties. For example, weak properness always holds for the toric quotient of a subtorus action on a toric variety whose fan has a convex support.