Let X be a smooth variety, E a locally free sheaf on X. We express the generating function of the motives [Quot (X) (E, n)] in terms of the power structure on the Grothendieck ring of varieties. This extends a recent result of Bagnarol, Fantechi and Perroni for curves, and a result of Gusein-Zade, Luengo and Melle-Hernandez for Hilbert schemes. We compute this generating function for curves and we express the relative motive [Quot(Ad)(partial derivative(circle times r)) -> Sym A(d)] as a plethystic exponential. (C) 2020 Elsevier Masson SAS. All rights reserved.
On the motive of the Quot scheme of finite quotients of a locally free sheaf / Ricolfi, A. T.. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 144:(2020), pp. 50-68. [10.1016/j.matpur.2020.10.001]
On the motive of the Quot scheme of finite quotients of a locally free sheaf
Ricolfi, A. T.
2020-01-01
Abstract
Let X be a smooth variety, E a locally free sheaf on X. We express the generating function of the motives [Quot (X) (E, n)] in terms of the power structure on the Grothendieck ring of varieties. This extends a recent result of Bagnarol, Fantechi and Perroni for curves, and a result of Gusein-Zade, Luengo and Melle-Hernandez for Hilbert schemes. We compute this generating function for curves and we express the relative motive [Quot(Ad)(partial derivative(circle times r)) -> Sym A(d)] as a plethystic exponential. (C) 2020 Elsevier Masson SAS. All rights reserved.| File | Dimensione | Formato | |
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