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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Our first result is that a homogeneous form $F$ in $n$ variables is GITsemistable with respect to the natural $SL(n)$-action if and only if the firstnon-trivial Hilbert point of the associated Milnor algebra is semistable. Wealso prove that the induced morphism on the GIT quotients is finite, andinjective on the locus of stable forms. Our second result is that theassociated form of $F$, also known as the Macaulay inverse system of the Milnoralgebra of $F$, and which is apolar to the last non-trivial Hilbert point ofthe Milnor algebra, is GIT semistable whenever $F$ is a smooth form. These tworesults answer questions of Alper and Isaev from arXiv:1407.6838.

GIT semistability of Hilbert points of Milnor algebras