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arXiv · 2102.05128

Rational normal curves and Hadamard products

Enrico Carlini·Maria Virginia Catalisano·Giuseppe Favacchio·Elena Guardo
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Abstract

Given $r>n$ general hyperplanes in $\mathbb P^n,$ a star configuration of points is the set of all the $n$-wise intersection of them. We introduce {\it contact star configurations}, which are star configurations where all the hyperplanes are osculating to the same rational normal curve. In this paper we find a relation between this construction and Hadamard products of linear varieties. Moreover, we study the union of contact star configurations on a same conic in $\mathbb P^2$, we prove that the union of two contact star configurations has a special $h$-vector and, in some cases, this is a complete intersection.

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Enrico Carlini, Maria Virginia Catalisano, Giuseppe Favacchio, Elena Guardo. 2021-02-09. Rational normal curves and Hadamard products. https://arxiv.org/abs/2102.05128

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