Restriction theorems for $\mu$-(semi)stable framed sheaves

TL;DR

This paper generalizes classical restriction theorems to the setting of $$-semistable framed sheaves, showing their stability is preserved under restriction to high-degree hypersurfaces.

Contribution

It extends Mehta-Ramanathan theorems to framed sheaves, establishing stability preservation under restriction in a more general context.

Findings

Restriction of $$-semistable framed sheaves remains $$-semistable on general high-degree hypersurfaces.

The result also applies to $$-stability with additional conditions.

The theorems hold on nonsingular projective irreducible varieties of dimension at least two.

Abstract

We provide a generalization of Mehta-Ramanathan theorems to framed sheaves: we prove that the restriction of a $\mu$-semistable framed sheaf on a nonsingular projective irreducible variety, of dimension greater or equal than two, to a general hypersurface of sufficiently high degree is again $\mu$-semistable. The same holds for $\mu$-stability under some additional assumptions.