Minimal decomposition of binary forms with respect to tangential projections

Details Minimal decomposition of binary forms with respect to tangential projections Minimal decomposition of binary forms with respect to tangential projections

2010-07-16

arxiv.org/abs/1007.2822v2

Mathematics

Algebraic Geometry

7 pages

Scientific paper

Let $C\subset \mathbb{P}^n$ be a rational normal curve and let $\ell_O:\mathbb{P}^{n+1}\dashrightarrow \mathbb{P}^n$ be any tangential projection form a point $O\in T_AC$ where $A\in C$. Hence $X:= \ell_O(C)\subset \mathbb{P}^n$ is a linearly normal cuspidal curve with degree $n+1$. For any $P = \ell_O(B)$, $B\in \mathbb{P}^{n+1}$, the $X$-rank $r_X(P)$ of $P$ is the minimal cardinality of a set $S\subset X$ whose linear span contains $P$. Here we describe $r_X(P)$ in terms of the schemes computing the $C$-rank or the border $C$-rank of $B$.

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