Hodge level for weighted complete intersections

TL;DR

This paper establishes lower bounds for Hodge numbers of smooth Fano weighted complete intersections, computes their Hodge level, and classifies varieties with Hodge numbers similar to projective spaces, curves, or low-dimensional Calabi-Yau varieties.

Contribution

It introduces a method to compute Hodge levels for these varieties and classifies those with Hodge numbers akin to well-understood geometric objects.

Findings

Hodge levels for certain classes of weighted complete intersections are computed.

Classification of varieties with Hodge numbers similar to projective spaces, curves, or low-dimensional Calabi-Yau varieties.

Lower bounds for Hodge numbers of smooth Fano weighted complete intersections are established.

Abstract

We give lower bounds for Hodge numbers of smooth well formed Fano weighted complete intersections. In particular, we compute their Hodge level, that is, the maximal distance between non-trivial Hodge numbers in the same row of the Hodge diamond. This allows us to classify varieties whose Hodge numbers are like that of a projective space, of a curve, or of a Calabi--Yau variety of low dimension.