Cartier modules on toric varieties
Author:
Abstract
Assume that X X is an affine toric variety of characteristic p > 0 p > 0 . Let Δ \Delta be an effective toric Q \mathbb {Q} -divisor such that K X + Δ K_X+\Delta is Q \mathbb {Q} -Cartier with index not divisible by p p and let ϕ Δ : F ∗ e O X → O X \phi _{\Delta }:F^e_*\mathscr {O}_X\to \mathscr {O}_X be the toric map corresponding to Δ \Delta . We identify all ideals I I of O X \mathscr {O}_X with ϕ Δ ( F ∗ e I ) = I \phi _{\Delta }(F^e_* I)=I combinatorially and also in terms of a log resolution (giving us a version of these ideals which can be defined in characteristic zero). Moreover, given a toric ideal a \mathfrak {a} , we identify all ideals I I fixed by the Cartier algebra generated by ϕ Δ \phi _{\Delta } and a \mathfrak {a} ; this answers a question by Manuel Blickle in the toric setting.
Publisher
American Mathematical Society (AMS)
Subject
Applied Mathematics,General Mathematics
Link
http://www.ams.org/tran/2014-366-04/S0002-9947-2013-05856-4/S0002-9947-2013-05856-4.pdf
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