The Chow Groups and the Motive of the Hilbert Scheme of Points on a Surface

By M. A. Cataldo, L. Migliorini. 2000

111 citations recorded by the source corpus.

Abstract We compute the Chow motive and the Chow groups with rational coefficients of the Hilbert scheme of points on a smooth algebraic surface.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6de47afcd875b0069f02c361d7fad057a38e097e

How researchers see this paper

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In Algebra and Number Theory

1. Charles Vial
2. Claire Voisin
3. D. Arapura
4. M. Shen
5. M. A. Cataldo
6. L. Migliorini
7. L. Fu
8. Zhiyu Tian

In Geometry and Topology

1. Charles Vial
2. Claire Voisin
3. M. Shen
4. L. Fu
5. M. A. Cataldo
6. L. Migliorini
7. D. Arapura
8. Zhiyu Tian

In Mathematical Physics

1. Charles Vial
2. Claire Voisin
3. L. Fu
4. M. Shen
5. M. A. Cataldo
6. L. Migliorini
7. D. Arapura
8. Zhiyu Tian

Citations in the corpus

• The Chow motive of semismall resolutions (2002, methodology): “In the former case, that determination had been done in [8] using the same correspondences, but additional knowledge was required, such as the affine cellular structure of the fibers, and the fact that the pre-image of each stratum maps locally trivially over the stratum in the étale topology.”
• Remarks And Questions On Coisotropic Subvarieties and 0-Cycles of Hyper-Kähler Varieties (2015, methodology): “In this case, there exists a natural splitting of the Bloch-Beilinson filtration which is given by the de CataldoMigliorini decomposition [10] and the decompositions of the motives of the ordinary selfproducts or symmetric products of S given by the choice of the class oS ∈ CH0(S) as in Section 2.”
• Motivation for Hodge cycles (2005, methodology): “For the Hilbert scheme of surface, this goes back to Cataldo-Migliorini [ CM ].”
• Chow Rings, Decomposition of the Diagonal, and the Topology of Families (2014, methodology): “From the work of de Cataldo and Migliorini [27], we know that the map”
• The Fourier Transform for Certain HyperKähler Fourfolds (2013, result): “Note that the existence of a Chow–Künneth decomposition for the Hilbert scheme of length-n subschemes on a surface follows directly from the existence of a Chow–Künneth decomposition for surfaces [38] and from the work of de Cataldo and Migliorini [18].”
• Motivic hyper-Kähler resolution conjecture, I : Generalized Kummer varieties (2016, methodology): “The result we need for Step (i) is de Cataldo–Migliorini [20, Theorem 1.0.1].”