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

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.

v2: incorporates changes suggested by the referee. v3: some intermediate results on the (relative) Harder-Narasimhan filtration and the Jordan-Holder filtrations have been extended to the case of framed sheaves on schemes. The main results are unchanged. To appear in Journal of Pure and Applied Algebra

References in corpus (1)

• Vertex Operators and Moduli Spaces of Sheaves

Cited by in corpus (2)

• Uhlenbeck-Donaldson compactification for framed sheaves on projective surfaces
• Metha-Ramanathan for ε and k-semistable Decorated Sheaves