Virtual classes and virtual motives of Quot schemes on threefolds

Abstract

For a simple, rigid vector bundle F on a Calabi–Yau 3-fold Y, we construct a symmetric obstruction theory on the Quot scheme QuotY(F,n), and we solve the associated enumerative theory. We discuss the case of other 3-folds. Exploiting the critical structure on the local model QuotAjavax.xml.bind.JAXBElement@e117367(O⊕r,n), we construct a virtual motive (in the sense of Behrend–Bryan–Szendrői) for QuotY(F,n) for an arbitrary vector bundle F on a smooth 3-fold Y. We compute the associated motivic partition function. We obtain new examples of higher rank (motivic) Donaldson–Thomas invariants.