Linear restrictions on cone polynomials

Weibo Fu; Zipei Nie

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arXiv · 1510.04630

Linear restrictions on cone polynomials

Weibo Fu·Zipei Nie

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Abstract

For a set $S$ of $d$ points in the $n$-dimensional projective space over a field of characteristic zero, we prove that the polynomials of degree $d$ whose zero sets are cones over $S$ do not span the vector space of polynomials of degree $d$ vanishing on $S$, if $d$ is odd and $d\ge 3$. Furthermore, they span a subspace of codimension at least two, if $n=2$, $d=1\pmod 4$ and $d\ge 5$.

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BibTeX RIS

Weibo Fu, Zipei Nie. 2015-10-15. Linear restrictions on cone polynomials. https://arxiv.org/abs/1510.04630

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