Mirror duality and string-theoretic Hodge numbers
Victor V. Batyrev, Lev A. Borisov
TL;DR
This paper proves the mirror-duality conjecture for string-theoretic Hodge numbers of Calabi-Yau complete intersections in Gorenstein toric Fano varieties. It develops a combinatorial framework using Eulerian posets and $B$-polynomials, derives an explicit formula for the E-polynomials of affine toric hypersurfaces via intersection cohomology, and extends to Calabi-Yau complete intersections defined by nef-partitions. The central result shows $E_{\rm st}(V;u,v)=(-u)^{d-r}E_{\rm st}(W;u^{-1},v)$ for mirror pairs, implying $h^{p,q}_{\rm st}(V)=h^{d-r-p,q}_{\rm st}(W)$, thereby validating the duality in full generality. The work provides a robust computational bridge between toric geometry, combinatorics, and string-theoretic invariants with potential physical interpretations.
Abstract
We prove in full generality the mirror duality conjecture for string-theoretic Hodge numbers of Calabi-Yau complete intersections in Gorenstein toric Fano varieties. The proof is based on properties of intersection cohomology