A Note on $h^{2,1}$ of Divisors of CY Fourfolds I

Abstract

In this note, we prove combinatorial formulas for $h^{2,1}$ 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 CICYs are the subjects of the part two.

v2. References added

References in corpus (7)

• Holographic Action for the Self-Dual Field
• F-theory uplifts and GUTs
• New F-theory lifts
• Conifold Vacua with Small Flux Superpotential
• The Vertical, the Horizontal and the Rest: anatomy of the middle cohomology of Calabi-Yau fourfolds and F-theory applications
• Small Flux Superpotentials for Type IIB Flux Vacua Close to a Conifold
• Tropical contractions to integral affine manifolds with singularities

Cited by in corpus (1)

• D-instanton, threshold corrections, and topological string