Quotients of Divisorial Toric Varieties
A. A'Campo-Neuen, J. Hausen

TL;DR
This paper studies subtorus actions on divisorial toric varieties, providing a characterization for when such actions admit categorical quotients, and introduces a universal reduction technique using support maps.
Contribution
It generalizes previous results for quasiprojective cases by characterizing quotients in divisorial toric varieties and develops a universal reduction method via support maps.
Findings
Characterization of subtorus actions admitting categorical quotients
Universal reduction of toric varieties to divisorial ones
Decomposition of invariant maps into toric and non-toric parts
Abstract
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Algebraic structures and combinatorial models
