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no. 5
Complement to Tautological classes on moduli spaces of hyper-Kähler manifolds
Nicolas Bergeron1; Zhiyuan Li2
1 ENS / PSL University, Département de Mathématiques et Applications, F-75005, Paris, France
2 Shanghai Center for Mathematical Sciences, Fudan University, 220 Handan Road, Shanghai, 200433 China
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 32 (2023) no. 5, pp. 839-854.

In this note we prove the cohomological tautological conjecture on moduli spaces of K3 and K3 [2] -type hyper-Kähler manifolds. That this result holds was first asserted in [2]. However the proof given there contains a gap, see [3]. Here we give a more direct proof.

Dans cette note nous démontrons, dans sa version cohomologique, la conjecture tautologique pour les espaces de modules des variétés hyper-Kähleriennes de type K3 et K3 [2] . Ce théorème est l’un des deux résultats principaux de [2]. Cependant la démonstration qui y est donnée comporte un trou que nous ne savons pas comblé, voir [3]. Nous donnons ici une preuve plus directe.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1755

Nicolas Bergeron 1; Zhiyuan Li 2

1 ENS / PSL University, Département de Mathématiques et Applications, F-75005, Paris, France
2 Shanghai Center for Mathematical Sciences, Fudan University, 220 Handan Road, Shanghai, 200433 China
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Nicolas Bergeron; Zhiyuan Li. Complement to Tautological classes on moduli spaces of hyper-Kähler manifolds. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 32 (2023) no. 5, pp. 839-854. doi : 10.5802/afst.1755. https://afst.centre-mersenne.org/articles/10.5802/afst.1755/

[1] Thorsten Beckmann Derived categories of hyper-Kähler manifolds: extended Mukai vector and integral structure, Compos. Math., Volume 159 (2023) no. 1, pp. 109-152 | DOI | MR | Zbl

[2] Nicolas Bergeron; Zhiyuan Li Tautological classes on moduli spaces of hyper-Kähler manifolds, Duke Math. J., Volume 168 (2019) no. 7, pp. 1179-1230 | Zbl

[3] Nicolas Bergeron; Zhiyuan Li Tautological classes on moduli spaces of hyper-Kähler manifolds. Erratum, Duke Math. J., Volume 171 (2022) no. 1, pp. 243-245

[4] Nicolas Bergeron; Zhiyuan Li; John Millson; Colette Moeglin The Noether–Lefschetz conjecture and generalizations, Invent. Math., Volume 208 (2017) no. 2, pp. 501-552 | DOI | MR

[5] Mark Andrea A. de Cataldo Hodge-theoretic splitting mechanisms for projective maps, J. Singul., Volume 7 (2013), pp. 134-156 | MR

[6] Claire Voisin Chow rings and decomposition theorems for families of K3 surfaces and Calabi–Yau hypersurfaces, Geom. Topol., Volume 16 (2012) no. 1, pp. 433-473 | DOI | MR | Zbl

[7] Yuri G. Zarkhin Hodge groups of K3 surfaces, J. Reine Angew. Math., Volume 341 (1983), pp. 193-220 | MR

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