Lie Fu ; Ben Moonen - Algebraic cycles on Gushel-Mukai varieties

epiga:9815 - Épijournal de Géométrie Algébrique, July 2, 2024, Special volume in honour of Claire Voisin - https://doi.org/10.46298/epiga.2024.9815
Algebraic cycles on Gushel-Mukai varietiesArticle

Authors: Lie Fu ; Ben Moonen

    We study algebraic cycles on complex Gushel-Mukai (GM) varieties. We prove the generalised Hodge conjecture, the (motivated) Mumford-Tate conjecture, and the generalised Tate conjecture for all GM varieties. We compute all integral Chow groups of GM varieties, except for the only two infinite-dimensional cases (1-cycles on GM fourfolds and 2-cycles on GM sixfolds). We prove that if two GM varieties are generalised partners or generalised duals, their rational Chow motives in middle degree are isomorphic.


    Volume: Special volume in honour of Claire Voisin
    Published on: July 2, 2024
    Accepted on: January 29, 2024
    Submitted on: July 20, 2022
    Keywords: Mathematics - Algebraic Geometry,14C15, 14C25, 14C30, 14J45, 14F08
    Funding:
      Source : OpenAIRE Graph
    • Fundamental Groups, Hodge Theory and Motives; Funder: French National Research Agency (ANR); Code: ANR-16-CE40-0011
    • From Fano to hyperKähler varieties: geometry and derived categories; Funder: French National Research Agency (ANR); Code: ANR-20-CE40-0023

    Consultation statistics

    This page has been seen 120 times.
    This article's PDF has been downloaded 70 times.