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arXiv · 1204.0475

Star configurations on generic hypersurfaces

Enrico Carlini·Elena Guardo·Adam Van Tuyl
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Abstract

Let $F$ be a homogeneous polynomial in $S = \mathbb{C}[x_0,...,x_n]$. Our goal is to understand a particular polynomial decomposition of $F$; geometrically, we wish to determine when the hypersurface defined by $F$ in $\mathbb{P}^n$ contains a star configuration. To solve this problem, we use techniques from commutative algebra and algebraic geometry to reduce our question to computing the rank of a matrix.

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Enrico Carlini, Elena Guardo, Adam Van Tuyl. 2012-04-02. Star configurations on generic hypersurfaces. https://arxiv.org/abs/1204.0475

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