Vector Bundles on non-K\"ahler elliptic principal bundles

TL;DR

This paper investigates the properties and moduli of semi-stable vector bundles on non-Kähler elliptic principal bundles, utilizing advanced techniques like twisted Fourier-Mukai transforms and spectral covers, with explicit computations for specific examples.

Contribution

It introduces a framework for studying vector bundles on non-Kähler elliptic principal bundles and computes numerical invariants for a key example, advancing understanding in complex geometry.

Findings

Computed numerical invariants for a 3D non-Kähler elliptic principal bundle over a primary Kodaira surface.

Developed a spectral cover construction for vector bundles in this non-Kähler setting.

Applied twisted Fourier-Mukai transform to analyze semi-stability and moduli of vector bundles.

Abstract

We study relatively semi-stable vector bundles and their moduli on non-K\"ahler principal elliptic bundles over compact complex manifolds of arbitrary dimension. The main technical tools used are the twisted Fourier-Mukai transform and a spectral cover construction. For the important example of such principal bundles, the numerical invariants of a 3-dimensional non-K\"ahler elliptic principal bundle over a primary Kodaira surface are computed.