Virtual classes and virtual motives of Quot schemes on threefolds

For a simple, rigid vector bundle F on a Calabi-Yau 3-fold Y, we construct a symmetric obstruction theory on the Quot scheme Quot(Y) (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 Quot(A3)(O-circle plus r,n), we construct a virtual motive (in the sense of Behrend-Bryan-Szendroi) for Quot(Y) (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. (C) 2020 Elsevier Inc. All rights reserved.