Abstract: |
Donaldson-Thomas invariants appear in the enumerative geometry of 3-folds as virtual counting performed over moduli spaces of sheaves with a perfect obstruction theory. In the case of the Hilbert scheme of points, a closed formula for the generating series of DT invariants was conjectured by Maulik-Nekrasov-Okounkov-Pandharipande and proved for toric 3-folds. Recently, a K-theoretic refinement of such invariants, motivated by string-theoretic phenomena, was conjectured by Nekrasov and proved by Okounkov. In our work, we generalize the theory to the Quot scheme of points of a locally free sheaf of arbitrary rank, proving closed higher rank formulae for the resulting invariants both in the classical and K-theoretic setting. Joint work with N. Fasola and A.T. Ricolfi. |