Hodge Numbers of Complete Intersections in Toric Varieties

We are interested in computing the Hodge numbers of divisors of complete intersections in toric varieties following the work of Danilov and Khovanskii using the technique of stratification.

As a special case, we will work with Calabi-Yau hypersurfaces in toric varieties corresponding to reflexive polytopes. The geometry of such hypersurfaces are particularly important in physics, having widespread applications in cosmology such as studying large field inflationary models to string/particle phenomenology and F-theory model building.

The seminal work of Danilov and Khovanskii, as well as Batyrev's work on mirror symmetry allows us to compute the Hodge-Deligne numbers and hence the Hodge diamond of divisors on complete intersections in toric varieties in terms of the combinatorial properties of the corresponding newton polyhedra. We plan to build a package that computationally computes the Hodge numbers of arbitrary sums of distinct such divisors.