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15 May 2019 Tautological classes on moduli spaces of hyper-Kähler manifolds
Nicolas Bergeron, Zhiyuan Li
Duke Math. J. 168(7): 1179-1230 (15 May 2019). DOI: 10.1215/00127094-2018-0063

Abstract

We study algebraic cycles on moduli spaces Fh of h-polarized hyper-Kähler manifolds. Following previous work of Marian, Oprea, and Pandharipande on the tautological conjecture on moduli spaces of K3 surfaces, we first define the tautological ring on Fh. We then study the images of these tautological classes in the cohomology groups of Fh and prove that most of them are linear combinations of Noether–Lefschetz cycle classes. In particular, we prove the cohomological version of the tautological conjecture on moduli space of K3[n]-type hyper-Kähler manifolds with n2. Secondly, we prove the cohomological generalized Franchetta conjecture on a universal family of these hyper-Kähler manifolds.

Citation

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Nicolas Bergeron. Zhiyuan Li. "Tautological classes on moduli spaces of hyper-Kähler manifolds." Duke Math. J. 168 (7) 1179 - 1230, 15 May 2019. https://doi.org/10.1215/00127094-2018-0063

Information

Received: 10 April 2017; Revised: 4 December 2018; Published: 15 May 2019
First available in Project Euclid: 27 April 2019

zbMATH: 07078882
MathSciNet: MR3953432
Digital Object Identifier: 10.1215/00127094-2018-0063

Subjects:
Primary: 14J28
Secondary: 11G18, 14C25, 14D20

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 7 • 15 May 2019
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