An example of liftings with different Hodge numbers

TL;DR

This paper presents an example of a smooth proper variety in positive characteristic that admits two different liftings, each with distinct Hodge numbers, highlighting variability in lifting properties.

Contribution

It provides a concrete example demonstrating that liftings of varieties can have different Hodge numbers, which was previously unknown.

Findings

Existence of a variety with two liftings having different Hodge numbers

Illustration of variability in Hodge numbers among liftings

Contribution to understanding deformation theory in positive characteristic

Abstract

In this paper, we exhibit an example of a smooth proper variety in positive characteristic possessing two liftings with different Hodge numbers.