A note on restriction theorems for semistable sheaves

TL;DR

This paper establishes new restriction theorems for semistable sheaves, including strong semistability, applicable across all characteristics and for varieties with certain cotangent bundle properties, advancing the understanding of sheaf stability.

Contribution

It introduces a strengthened restriction theorem for semistable sheaves and extends results to strong semistability on specific varieties with non-negative cotangent bundles.

Findings

Proved a new restriction theorem for semistable sheaves in all characteristics.

Established restriction theorem for strong semistability on Fano and Calabi-Yau varieties.

Extended the applicability of restriction theorems to varieties with non-negative cotangent bundles.

Abstract

We prove a new restriction theorem for semistable sheaves on varieties in all characteristics strengthening previous results. We also prove restriction theorem for strong semistability for varieties with some non-negativity constrains on the cotangent bundle (e.g., most of Fano and Calabi-Yau varieties).