Let X be a smooth variety, E a locally free sheaf on X. We express the generating function of the motives [QuotX(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-Hernández for Hilbert schemes. We compute this generating function for curves and we express the relative motive [QuotAjavax.xml.bind.JAXBElement@13d85294(O⊕r)→SymAd] as a plethystic exponential.
Ricolfi A.T. (2020). On the motive of the Quot scheme of finite quotients of a locally free sheaf. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES, 144, 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
Abstract
Let X be a smooth variety, E a locally free sheaf on X. We express the generating function of the motives [QuotX(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-Hernández for Hilbert schemes. We compute this generating function for curves and we express the relative motive [QuotAjavax.xml.bind.JAXBElement@13d85294(O⊕r)→SymAd] as a plethystic exponential.File | Dimensione | Formato | |
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