On the motive of the Quot scheme of finite quotients of a locally free\n sheaf

2019/07/18 by Andrea T. Ricolfi, Ricolfi, Andrea T. · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1907.08123

openalex publication_date 2019/07/18 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth variety, E a locally free sheaf on X. We express the\ngenerating function of the motives [ textrmQuot_X(E,n)] in terms of the\npower structure on the Grothendieck ring of varieties. This extends a recent\nresult of Bagnarol, Fantechi and Perroni for curves, and a result of\nGusein-Zade, Luengo and Melle-Hern 'andez for Hilbert schemes. We compute\nthis generating function for curves and we express the relative motive\n[ textrmQuot _{mathbb A^d}( mathscrO^{\⊕ r}) \→ textrmSym ,\n mathbb A^d] as a plethystic exponential.\n

Cited by

• The Iarrobino scheme: a self-dual analogue of the Hilbert scheme of points

Related

• On the motive of zero-dimensional Quot schemes on a curve
• Motivic classes of Quot-schemes on surfaces
• Hyperquot schemes on curves: virtual class and motivic invariants
• On the motive of quotients of induced actions
• Effective Grothendieck-Witt motives of smooth varieties