Kieran G. O'Grady - Rank 4 stable vector bundles on hyperkähler fourfolds of Kummer type

epiga:10857 - Épijournal de Géométrie Algébrique, December 5, 2024, Special volume in honour of Claire Voisin - https://doi.org/10.46298/epiga.2024.10857
Rank 4 stable vector bundles on hyperkähler fourfolds of Kummer typeArticle

Authors: Kieran G. O'Grady

    We partially extend to hyperkähler fourfolds of Kummer type the results that we have proved regarding stable rigid vector bundles on hyperkähler (HK) varieties of type $K3^{[n]}$. Let $(M,h)$ be a general polarized HK fourfold of Kummer type such that $q_M(h)\equiv -6\pmod{16}$ and the divisibility of $h$ is $2$, or $q_M(h)\equiv -6\pmod{144}$ and the divisibility of $h$ is $6$. We show that there exists a unique (up to isomorphism) slope stable vector bundle $\cal F$ on $M$ such that $r({\cal F})=4$, $ c_1({\cal F})=h$, $\Delta({\cal F})=c_2(M)$. Moreover $\cal F$ is rigid. One of our motivations is the desire to describe explicitly a locally complete family of polarized HK fourfolds of Kummer type.


    Volume: Special volume in honour of Claire Voisin
    Published on: December 5, 2024
    Accepted on: September 11, 2024
    Submitted on: January 26, 2023
    Keywords: Mathematics - Algebraic Geometry,14J42 (Primary), 14J60 (Secondary)

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