Assume that X is an affine toric variety of characteristic p > 0. Let Δ be an effective toric ℚ-divisor such that KX +Δ is ℚ-Cartier with index not divisible by p and let φΔ: F*e ∂X → ∂X be the toric map corresponding to Δ. We identify all ideals I of ∂X with φΔ(F*eI) = 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, we identify all ideals I fixed by the Cartier algebra generated by φ Δ and a; this answers a question by Manuel Blickle in the toric setting.
All Science Journal Classification (ASJC) codes
- Applied Mathematics