A note on h2,1 of divisors in CY fourfolds. Part I

In this note, we prove combinatorial formulas for the Hodge number h(2,1) of prime toric divisors in an arbitrary toric hypersurface Calabi-Yau fourfold Y-4. We show that it is possible to find a toric hypersurface Calabi-Yau in which there are more than h(1,1)(Y-4) non-perturbative superpotential terms with trivial intermediate Jacobian. Hodge numbers of divisors in toric complete intersection Calabi-Yaus are the subjects of the sequel.

Automated summary

In this note, we prove combinatorial formulas for the Hodge number h(2,1) of prime toric divisors in an arbitrary toric hypersurface Calabi-Yau fourfold Y-4. We show that it is possible to find a toric hypersurface Calabi-Yau in which there are more than h(1,1)(Y-4) non-perturbative superpotential terms with trivial intermediate Jacobian.