English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We first prove an isomorphism between the moduli space of smooth cubicthreefolds and the moduli space of hyperkaehler fourfolds of K3^{[2]}-type witha non-symplectic automorphism of order three, whose invariant lattice has rankone and is generated by a class of square 6, both these spaces are uniformizedby the same 10-dimensional arithmetic complex ball quotient. We then study thedegeneration of the automorphism along the loci of nodal or chordaldegenerations of the cubic threefold, showing the birationality of these lociwith some moduli spaces of hyperkaehler fourfolds of K3^{[2]}-type withnon-symplectic automorphism of order three belonging to different families.Finally, we construct a cyclic Pfaffian cubic fourfold to give an explicitconstruction of a non-natural automorphism of order three on the Hilbert squareof a K3 surface.

Cubic threefolds and hyperk\"ahler manifolds uniformized by the 10-dimensional complex ball