Star configurations on generic hypersurfaces

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.

17 pages