On the saturation sequence of the rational normal curve

Details On the saturation sequence of the rational normal curve On the saturation sequence of the rational normal curve

2009-10-02

arxiv.org/abs/0910.0298v1

Mathematics

Algebraic Geometry

Scientific paper

Let $C \subseteq \P^d$ denote the rational normal curve of order $d$. Its homogeneous defining ideal $I_C \subseteq \QQ[a_0,...,a_d]$ admits an $SL_2$-stable filtration $J_2 \subseteq J_4 \subseteq ... \subseteq I_C$ by sub-ideals such that the saturation of each $J_{2q}$ equals $I_C$. Hence, one can associate to $d$ a sequence of integers $(\alpha_1,\alpha_2,...)$ which encodes the degrees in which the successive inclusions in this filtration become trivial. In this paper we establish several lower and upper bounds on the $\alpha_q$, using \emph{inter alia} the methods of classical invariant theory.

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