52 research outputs found
GIT semistability of Hilbert points of Milnor algebras
Our first result is that a homogeneous form in variables is GIT
semistable with respect to the natural -action if and only if the first
non-trivial Hilbert point of the associated Milnor algebra is semistable. We
also prove that the induced morphism on the GIT quotients is finite, and
injective on the locus of stable forms. Our second result is that the
associated form of , also known as the Macaulay inverse system of the Milnor
algebra of , and which is apolar to the last non-trivial Hilbert point of
the Milnor algebra, is GIT semistable whenever is a smooth form. These two
results answer questions of Alper and Isaev from arXiv:1407.6838.Comment: 19 pages, to appear in Math. An
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