Hyperk\"ahler Manifolds of Curves in Twistor Spaces

TL;DR

This paper explores how higher degree curves in complex fibrations over the projective line can be used to construct hypercomplex and hyperk"ahler structures, advancing understanding of geometric structures in complex spaces.

Contribution

It introduces a novel approach to deriving hyperk"ahler structures from higher degree curves in complex fibrations over ${ m P}^1$, expanding the methods for constructing such geometries.

Findings

Construction of hyperk"ahler structures from higher degree curves

Extension of hypercomplex structures in complex fibrations

New insights into geometric structures on complex spaces

Abstract

We discuss hypercomplex and hyperk\"ahler structures obtained from higher degree curves in complex spaces fibring over ${\mathbb{P}}^1$.