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Quotients of Divisorial Toric Varieties | | A. A’Campo-Neuen
; J. Hausen
; | | Date: |
24 Dec 1999 | | Journal: | Michigan Math. J. 50, No 1., 101-123 (2002) | | Subject: | Algebraic Geometry MSC-class: 14L30; 14M25; 14C20 | math.AG | | 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. | | Source: | arXiv, math.AG/0001131 | | Services: | Forum | Review | PDF | Favorites | |
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