2000/01/31 by A. A'Campo-Neuen, J. Hausen
Mathematics · #math.AG #msc:14L30 #msc:14M25 #msc:14C20
published as Michigan Math. J. 50, No 1., 101-123 (2002) · 20 pages, LaTeX2e, 3 figures. Extended version including more examples. To appear in Michigan Math. J
arxiv created 2002/02/26 · arxiv updated 2009/11/30
We consider subtorus actions on divisorial toric varieties. Here divisoriality means that the variety has many Cartier divisors like quasiprojective and smooth ones. We characterize when a subtorus action on such a toric variety admits a categorical quotient in the category of divisorial varieties. Our result generalizes previous statements for the quasiprojective case. An important tool for the proof is a universal reduction of an arbitrary toric variety to a divisorial one. This is done in terms of support maps, a notion generalizing support functions on a polytopal fan. A further essential step is the decomposition of a given subtorus invariant regular map to a divisorial variety into an invariant toric part followed by a non-toric part.