Quotients of Divisorial Toric Varieties

Details Quotients of Divisorial Toric Varieties Quotients of Divisorial Toric Varieties

2000-01-24

arxiv.org/abs/math/0001131v3

Michigan Math. J. 50, No 1., 101-123 (2002)

Mathematics

Algebraic Geometry

20 pages, LaTeX2e, 3 figures. Extended version including more examples. To appear in Michigan Math. J

Scientific paper

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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