On the birational motive of hyper-Kahler varieties

Vial C (2022)
Journal de Mathématiques Pures et Appliquées 163: 577-624.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We introduce a new ascending filtration, that we call the co-radical filtration in analogy with the basic theory of co-algebras, on the Chow groups of pointed smooth projective varieties. In the case of zero-cycles on projective hyper-Kahler manifolds, we conjecture it agrees with a filtration introduced by Voisin. This is established for moduli spaces of stable objects on K3 surfaces, for generalized Kummer varieties and for the Fano variety of lines on a smooth cubic fourfold. Our overall strategy is to view the birational motive of a smooth projective variety as a co-algebra object with respect to the diagonal embedding and to show in the aforementioned cases the existence of a so-called strict grading whose associated filtration agrees with the filtration of Voisin. As results of independent interest, we upgrade to rational equivalence Voisin's notion of "surface decomposition" and show that the birational motive of some projective hyper-Kahler manifolds is determined, as a co-algebra object, by the birational motive of a surface. We also relate our co-radical filtration on the Chow groups of abelian varieties to Beauville's eigenspace decomposition.(c) 2022 Elsevier Masson SAS. All rights reserved.
Stichworte
Algebraic cycles; Hyper-K?hler varieties; Moduli spaces of sheaves on; K3; surfaces; Birational motives; Abelian varieties; Co-algebras
Erscheinungsjahr
2022
Zeitschriftentitel
Journal de Mathématiques Pures et Appliquées
Band
163
Seite(n)
577-624
ISSN
0021-7824
eISSN
1776-3371
Page URI
https://pub.uni-bielefeld.de/record/2964335

Zitieren

Vial C. On the birational motive of hyper-Kahler varieties. Journal de Mathématiques Pures et Appliquées. 2022;163:577-624.
Vial, C. (2022). On the birational motive of hyper-Kahler varieties. Journal de Mathématiques Pures et Appliquées, 163, 577-624. https://doi.org/10.1016/j.matpur.2022.05.015
Vial, C. (2022). On the birational motive of hyper-Kahler varieties. Journal de Mathématiques Pures et Appliquées 163, 577-624.
Vial, C., 2022. On the birational motive of hyper-Kahler varieties. Journal de Mathématiques Pures et Appliquées, 163, p 577-624.
C. Vial, “On the birational motive of hyper-Kahler varieties”, Journal de Mathématiques Pures et Appliquées, vol. 163, 2022, pp. 577-624.
Vial, C.: On the birational motive of hyper-Kahler varieties. Journal de Mathématiques Pures et Appliquées. 163, 577-624 (2022).
Vial, Charles. “On the birational motive of hyper-Kahler varieties”. Journal de Mathématiques Pures et Appliquées 163 (2022): 577-624.

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