We show that the Quot scheme QuotA3(Or, n) admits a symmetric obstruction theory, and we compute its virtual Euler characteristic. We extend the calculation to locally free sheaves on smooth 3-folds, thus refining a special case of a recent Euler characteristic calculation of Gholampour–Kool. We then extend Toda’s higher rank DT/PT correspondence on Calabi–Yau 3-folds to a local version centered at a fixed slope stable sheaf. This generalises (and refines) the local DT/PT correspondence around the cycle of a Cohen–Macaulay curve. Our approach clarifies the relation between Gholampour–Kool’s functional equation for Quot schemes, and Toda’s higher rank DT/PT correspondence.
Virtual counts on Quot schemes and the higher rank local DT/PT correspondence / Beentjes S.V.; Ricolfi A.T.. - In: MATHEMATICAL RESEARCH LETTERS. - ISSN 1073-2780. - STAMPA. - 28:4(2021), pp. 967-1032. [10.4310/MRL.2021.V28.N4.A2]
Virtual counts on Quot schemes and the higher rank local DT/PT correspondence
Ricolfi A. T.
2021
Abstract
We show that the Quot scheme QuotA3(Or, n) admits a symmetric obstruction theory, and we compute its virtual Euler characteristic. We extend the calculation to locally free sheaves on smooth 3-folds, thus refining a special case of a recent Euler characteristic calculation of Gholampour–Kool. We then extend Toda’s higher rank DT/PT correspondence on Calabi–Yau 3-folds to a local version centered at a fixed slope stable sheaf. This generalises (and refines) the local DT/PT correspondence around the cycle of a Cohen–Macaulay curve. Our approach clarifies the relation between Gholampour–Kool’s functional equation for Quot schemes, and Toda’s higher rank DT/PT correspondence.File | Dimensione | Formato | |
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