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- W2201743485 abstract "We study the category of KM - a generalization of the category of considered in toric geometry - and its various realization functors to geometric categories. The purest such realization takes the form of a functor from KM to the 2-category of stacks over the category of fine fans, in the characteristic-zero-'etale topology. In the algebraic setting, over a field of characteristic zero, we have a realization functor from KM to (log) Deligne-Mumford stacks. We prove that this realization functor gives rise to an equivalence of categories between (lattice) KM and an appropriate category of toric DM stacks. Finally, we have a differential realization functor to the category of (positive) log differentiable spaces. Unlike the other realizations, the differential realization of a fan is an actual log differentiable space, not a stack. Our main results are generalizations of classical toric geometry, as well as a characterization of when a map of KM is a torsor. The latter is used to explain the relationship between our theory and the stacky fans of Geraschenko and Satriano." @default.
- W2201743485 created "2016-06-24" @default.
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- W2201743485 date "2015-12-23" @default.
- W2201743485 modified "2023-10-06" @default.
- W2201743485 title "A Theory of Stacky Fans" @default.
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