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# Xuqiang Qin, UNC-Chapel Hill – Geometric Methods in Representation Theory Seminar

## November 12, 2021 @ 4:00 pm - 5:00 pm

**Mode:** In-Person

**Location:** Phillips Hall 385

**Title:** Minimal instantons on Fano threefolds and compactifications of their moduli spaces

**Abstract:**Instanton bundles were first introduced on P^3 as stable rank 2 bundles E with c1(E)=0 and H^1(E(-2))=0. Torsion free generalizations and properties of moduli spaces of instanton bundles have been widely studied. Faenzi and Kuznetsov generalized the notion of instanton bundles to other Fano threefolds. In this talk, we look at semistable sheaves of rank 2 with Chern classes c1 = 0, c2 = 2 and c3 = 0 on some Fano threefolds of Picard number 1 and index 2. We show that the moduli space of such sheaves provides a smooth compactification of the moduli space of minimal instanton bundles.