Gorenstein points in $${\mathbb {P}}^{3}$$ via Hadamard products of projective varieties
Abstract We show how to construct a stick figure of lines in $${\mathbb {P}}^3$$ P 3 using the Hadamard product of projective varieties. Then, applying the results of Migliore and Nagel, we use such a stick figure to build a Gorenstein set of points with given $$h-$$ h - vector $${\varvec{h}}$$ h ....
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| Published in | Collectanea mathematica (Barcelona) Vol. 74; no. 3; pp. 505 - 527 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
01.09.2023
|
| Online Access | Get full text |
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| Summary: | Abstract
We show how to construct a stick figure of lines in
$${\mathbb {P}}^3$$
P
3
using the Hadamard product of projective varieties. Then, applying the results of Migliore and Nagel, we use such a stick figure to build a Gorenstein set of points with given
$$h-$$
h
-
vector
$${\varvec{h}}$$
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. |
|---|---|
| ISSN: | 0010-0757 2038-4815 |
| DOI: | 10.1007/s13348-022-00362-9 |