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arXiv · 2109.10328

Gorenstein points in $\mathbb{P}^3$ via Hadamard product of projective varieties

Cristiano Bocci·Chiara Capresi·Daniele Carrucoli
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Abstract

We show how to construct a stick figure of lines in $\mathbb{P}^3$ using the Hadamard product of projective varieties. Then, applying the results of Migliore and Nagel, we use such stick figure to build a Gorenstein set of points with given $h-$vector ${\mathbf h}$. Since the Hadamard product is a coordinate-wise product, we show, at the end, how the coordinates of the points, in the Gorenstein set, can be directly determined.

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Cristiano Bocci, Chiara Capresi, Daniele Carrucoli. 2021-09-21. Gorenstein points in $\mathbb{P}^3$ via Hadamard product of projective varieties. https://arxiv.org/abs/2109.10328

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