Special Kahler Metrics on Complex Line Bundles and the Geometry of $K3$-Surfaces

TL;DR

This paper constructs special holonomy metrics on tangent bundles of weighted projective lines and explores the moduli space of such metrics on K3-surfaces, revealing new geometric structures near orbifold points.

Contribution

It introduces explicit constructions of SU(2) holonomy metrics on tangent bundles and describes the local geometry of the moduli space of special Kähler metrics on K3-surfaces.

Findings

Metrics with SU(2) holonomy on tangent bundles of weighted projective lines

Geometric description of the moduli space near flat orbifold points

Insights into the structure of K3-surface metrics

Abstract

We construct metrics with the holonomy group SU(2) on the tangent bundles of weighted complex projective lines and give a geometric description of the moduli space of special Kahler metrics on a K3-surface in the neighborhood of the flat orbifold $T^4/Z_3$.