Grassmannian BGG Complexes and Hodge numbers of irregular varieties

TL;DR

This paper studies the exactness of Grassmannian BGG complexes and derives inequalities for Hodge numbers of irregular varieties, providing sharp bounds for subvarieties of Abelian varieties and improving existing results on threefolds and fourfolds.

Contribution

It introduces new inequalities for Hodge numbers based on Grassmannian BGG complexes, enhancing understanding of irregular varieties and their subvarieties.

Findings

Sharp lower bounds for Hodge numbers of subvarieties of Abelian varieties

Improved inequalities for threefolds and fourfolds

Analysis of the exactness of Grassmannian BGG complexes

Abstract

In this paper we investigate the exactness of the Grassmannian BGG complexes introduced in a previous work (arXiv:1211.2486), and obtain some inequalities between some Hodge numbers of some irregular varieties. In particular, we obtain sharp lower bounds for the Hodge numbers of smooth subvarieties of Abelian varieties, as well as some improvements of results of Lazarsfeld and Popa and Lombardi concerning threefolds and fourfolds.