On the motive of zero-dimensional Quot schemes on a curve
On the motive of zero-dimensional Quot schemes on a curve
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曲线上零维报价方案的动机
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Fabio Perroni
中科院分区：
文献类型：
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作者：
Massimo Bagnarol;B. Fantechi;Fabio Perroni
对于任何局部自由相干层上的一个固定的光滑的射影曲线，我们研究类，在Grothendieck环的品种，报价计划参数化的零维相干层。我们证明了这个类只依赖于层的秩和同分元的长度。作为一个应用，我们得到了一个明确的公式，表示它的对称产品的曲线。
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.