Restrictions of stable bundles

TL;DR

This paper improves bounds on the degree requirements for restricting stable vector bundles to curves while maintaining stability, and proposes a conjecture for optimal bounds.

Contribution

It refines the Mehta-Ramanathan theorem by providing sharper bounds and introduces a conjecture for the best possible degree conditions.

Findings

Improved bounds for stable bundle restrictions

Proposed a conjecture on optimal degree bounds

Enhanced understanding of stability preservation

Abstract

The Mehta-Ramanathan theorem ensures that the restriction of a stable vector bundle to a sufficiently high degree complete intersection curve is again stable. We improve the bounds for the "sufficiently high degree" and propose a possibly optimal conjecture.