# Partial elimination ideals and secant cones - Mathematics > Commutative Algebra

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Abstract: For any $k \in \Nat$, we show that the cone of $k+1$-secant lines of aclosed subscheme $Z \subset \mathbb{P}^n K$ over an algebraically closed field$K$ running through a closed point $p \in \mathbb{P}^n K$ is defined by the$k$-th partial elimination ideal of $Z$ with respect to $p$. We use this factto give an algorithm for computing secant cones. Also, we show that undercertain conditions partial elimination ideals describe the length of the fibresof a multiple projection in a way similar to the way they do for simpleprojections. Finally, we study some examples illustrating these results,computed by means of {\sc Singular}.

Author: ** Simon Kurmann**

Source: https://arxiv.org/