For any locally free coherent sheaf on a fixed smooth projective curve, we study the class, in the Grothendieck ring of varieties, of the Quot scheme that parametrizes zero-dimensional quotients of the sheaf. We prove that this class depends only on the rank of the sheaf and on the length of the quotients. As an application, we obtain an explicit formula that expresses it in terms of the symmetric products of the curve.
On the motive of Quot schemes of zero-dimensional quotients on a curve / Bagnarol, M.; Fantechi, B.; Perroni, F.. - In: NEW YORK JOURNAL OF MATHEMATICS. - ISSN 1076-9803. - 26:(2020), pp. 138-148.
On the motive of Quot schemes of zero-dimensional quotients on a curve
Bagnarol, M.;Fantechi, B.;Perroni, F.
2020-01-01
Abstract
For any locally free coherent sheaf on a fixed smooth projective curve, we study the class, in the Grothendieck ring of varieties, of the Quot scheme that parametrizes zero-dimensional quotients of the sheaf. We prove that this class depends only on the rank of the sheaf and on the length of the quotients. As an application, we obtain an explicit formula that expresses it in terms of the symmetric products of the curve.File in questo prodotto:
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