On Hodge numbers of complete intersections and Landau--Ginzburg models

Abstract

We prove that the Hodge number $h^{1,N-1}(X)$ of an $N$-dimensional ($N⩾3$) Fano complete intersection $X$ is less by one then the number of irreducible components of the central fiber of (any) Calabi--Yau compactification of Givental's Landau--Ginzburg model for $X$.

arXiv comment23 pages, some misprints are corrected and improvements are made, comments are welcome