A continuity theorem for families of sheaves on complex surfaces

Nicholas Buchdahl, Andrei Teleman, Matei Toma

We prove that any flat family $({\mathcal{F}}_u{)}_{u\in U}$ of rank 2 torsion-free sheaves on a Gauduchon surface defines a continuous map on the semi-stable locus $U^{\mathrm {ss}}:…