Approximation of semistable bundles on smooth algebraic varieties

TL;DR

This paper proves strong approximation results for strongly semistable bundles with vanishing Chern classes on smooth algebraic varieties, generalizing previous work on curves and surfaces and confirming a conjecture.

Contribution

It extends earlier results to higher-dimensional varieties, providing new approximation techniques for semistable bundles with specific properties.

Findings

Approximation of semistable bundles by filtrations with line bundle quotients

Generalization of curve and surface case results to higher dimensions

Confirmation of the conjecture by Koley and Parameswaran

Abstract

We prove some strong results on approximation of strongly semistable bundles with vanishing numerical Chern classes by filtrations, whose quotients are line bundles of similar slope. This generalizes some earlier results of Parameswaran-Subramanian in the curve case and Koley-Parameswaran in the surface case and it confirms the conjecture posed by Koley and Parameswaran.