A restriction theorem for torsion-free sheaves on some elliptic manifolds

TL;DR

This paper proves that on certain non-Kähler elliptic principal bundles, torsion-free sheaves restrict to semi-stable sheaves on general fibers, revealing stability properties in complex geometry.

Contribution

It establishes a restriction theorem for torsion-free sheaves on non-Kähler elliptic manifolds, a new result in the study of stability in complex geometry.

Findings

Torsion-free sheaves restrict to semi-stable sheaves on general fibers

Applicable to non-Kähler elliptic principal bundles

Advances understanding of sheaf stability in complex manifolds

Abstract

We prove that if $X$ is the total space of an elliptic principal bundle $\pi:X\ra B$ which is non-K\"ahler, then the restriction of any torsion-free sheaf on $X$ to the general fiber of $\pi$ is semi-stable.