2022/03/08 by Kieran G. O'Grady, Kieran G. O’Grady · 1 citation
Mathematics · #math.AG #msc:14J42 #msc:14J60
paper · pdf · doi:10.46298/epiga.2024.10857
published as Épijournal de Géométrie Algébrique, Special volume in honour of Claire Voisin (December 5, 2024) epiga:10857 · The present version is the final version, as it will appear on Epiga
arxiv created 2024/12/04 · arxiv updated 2026/08/05
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 qM(h)≡ -6\pmod16 and the divisibility of h is 2, or qM(h)≡ -6\pmod144 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, c1(\cal F)=h, Δ(\cal F)=c2(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.