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

TL;DR

This paper establishes a relationship between the Hodge number of Fano complete intersections and the structure of Landau-Ginzburg models, revealing a new geometric connection in mirror symmetry.

Contribution

It proves that the Hodge number h^{1,N-1}(X) is exactly one less than the number of irreducible components of the central fiber of the Calabi-Yau compactification of Givental's Landau-Ginzburg model for X.

Findings

Hodge number h^{1,N-1}(X) is determined by Landau-Ginzburg model components.

The central fiber's irreducible components count relates directly to Hodge numbers.

Provides a new geometric insight into mirror symmetry for Fano varieties.

Abstract

We prove that the Hodge number $h^{1,N-1}(X)$ of an $N$-dimensional ($N\geqslant 3$) 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 $X$.