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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Elina Robeva discovered quadratic equations satisfied by orthogonallydecomposable ("odeco") tensors. Boralevi-Draisma-Horobe\c{t}-Robeva then provedthat, over the real numbers, these equations characterise odeco tensors. Thisraises the question to what extent they also characterise the Zariski-closureof the set of odeco tensors over the complex numbers. In the current paper werestrict ourselves to symmetric tensors of order three, i.e., of format $n\times n \times n$. By providing an explicit counterexample to one of Robeva'sconjectures, we show that for $n \geq 12$, these equations do not suffice.Furthermore, in the open subset where the linear span of the slices of thetensor contains an invertible matrix, we show that Robeva's equations cut outthe limits of odeco tensors for dimension $n \leq 13$, and not for $n \geq 14$on. To this end, we show that Robeva's equations essentially capture theGorenstein locus in the Hilbert scheme of $n$ points and we use work byCasnati-Jelisiejew-Notari on the (ir)reducibility of this locus.

On the quadratic equations for odeco tensors