Description
I will describe a systematic combinatorial construction of O3/O7 orientifolds of Calabi-Yau hypersurfaces in toric varieties and of their corresponding F-theory uplifts. Starting from toric fourfolds associated to four-dimensional reflexive polytopes, the orientifold involutions can be classified combinatorially, while the F-theory uplifts arise as codimension-two complete intersections in toric sixfolds. A key ingredient is the use of normal fans to control the birational phases of the Calabi-Yau threefold, ensuring smoothness of the resulting Calabi-Yau fourfold away from loci associated with O3-planes. In many cases, these uplifts are moreover described by nef partitions of six-dimensional reflexive polytopes, allowing the computation of fourfold periods and the associated F-theory flux superpotential.
