Projective structures on moduli spaces of compact complex hypersurfaces

TL;DR

This paper demonstrates that moduli spaces of complete families of compact complex hypersurfaces naturally possess projective structures that meet certain integrability conditions, revealing new geometric properties of these moduli spaces.

Contribution

It introduces the existence of canonical projective structures on moduli spaces of compact complex hypersurfaces, highlighting their natural integrability.

Findings

Moduli spaces often have canonical projective structures.

These structures satisfy natural integrability conditions.

The result applies to complete families of hypersurfaces.

Abstract

It is shown that moduli spaces of complete families of compact complex hypersurfaces in complex manifolds often come equipped canonically with projective structures satisfying some natural integrability conditions.