Holomorphic parabolic geometries on smooth projective varieties

TL;DR

This paper classifies holomorphic parabolic geometries on compact complex manifolds of general type, establishing bounds based on geometric invariants and revealing associated foliations and fibrations.

Contribution

It provides a classification of such geometries on projective varieties of general type and introduces bounds using invariants of the flag variety model.

Findings

Bounded the numerical dimension of varieties with holomorphic parabolic geometries

Identified foliations and fibrations compatible with these geometries

Established relationships between geometries and flag variety invariants

Abstract

We classify the holomorphic parabolic geometries on compact complex manifolds of general type. We accomplish this by bounding the numerical dimension of any smooth projective variety in terms of geometric invariants of the flag variety model of any holomorphic parabolic geometry on that variety. Along the way, we uncover foliations and fibrations on smooth projective varieties that admit holomorphic parabolic geometries.