Stable rationality of hypersurfaces of mock toric variety I

Abstract

We introduce a mock toric variety, a generalization of a toric variety. For a non-toric example, Del-Pezzo surfaces are mock toric varieties. These new varieties inherit some properties of mock toric varieties. In application, we give sufficient conditions for the concrete construction of a strictly toroidal model of a hypersurface in a mock toric variety.

83 pages. I have added new results to the end-of-2023 version and resubmitted the first of the two split papers as a replacement for that version. The second half will be posted on arXiv shortly