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.
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. - STAMPA. - 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
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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1907.08123.pdf
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