Holomorphic normal projective connections on projective manifolds

TL;DR

This paper investigates projective manifolds with flat holomorphic normal projective connections, revealing that their Iitaka fibration induces a smooth abelian group scheme structure, up to etale coverings.

Contribution

It establishes a link between flat holomorphic projective connections and abelian group scheme structures on projective manifolds, expanding understanding of their geometric properties.

Findings

Iitaka fibration defines a smooth abelian group scheme structure

Manifolds admit a flat holomorphic normal projective connection

Results hold up to etale coverings

Abstract

We study projective manifolds M admitting a (flat) holomorphic normal projective connection and show that the Iitaka fibration (up to etale coverings) defines a smooth abelian group scheme structure on M.