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 study the behaviour on some nodal hyperplanes of the isomorphism,described in a paper of 2019 by Boissi\`ere, Camere and Sarti, between themoduli space of smooth cubic threefolds and the moduli space of hyperk\"ahlerfourfolds of $K3^{[2]}$-type with a non-symplectic automorphism of order three,whose invariant lattice has rank one and is generated by a class of square 6;along those hyperplanes the automorphism degenerates by jumping to anotherfamily. We generalize their result to singular nodal cubic threefolds havingone singularity of type $A_i$ for $i=2, 3, 4$ providing birational maps betweenthe loci of cubic threefolds where a generic element has an isolatedsingularity of the types $A_i$ and some moduli spaces of hyperk\"ahlerfourfolds of $K3^{[2]}$-type with non-symplectic automorphism of order threebelonging to different families. In order to treat the $A_2$ case, we introducethe notion of K\"ahler cone sections of $K$-type generalizing the definition of$K$-general polarized hyperk\"ahler manifolds.

GIT stable cubic threefolds and certain fourfolds of $K3^{[2]}$-type