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Hadamard star configurations. (English) Zbl 1423.14297

Let \(X, Y\subset \mathbb{P}^n\) be varieties. The Hadamard product of \(X\) and \(Y\) inside \(\mathbb{P}^n\) is the closure inside \(\mathbb{P}^n\) of the rational map \(X\times Y\dashrightarrow \mathbb{P}^n\) defined by the formula \(([x_0:\dots :x_n],[y_0:\dots: y_n])\mapsto [x_0y_0:\dots:x_ny_n]\), with \([x_0:\dots :x_n]\in X\) and \([y_0:\dots:y_n]\in Y\) ([J. Kileel et al., Found. Comput. Math. 18, No. 4, 1043–1071 (2018; Zbl 1408.14191)]).
The authors use the Hadamard product to construct certain \(\ast\)-configuration of codimension \(c\) linear subspaces of \(\mathbb {P}^n\), generalizing the case \(n=c=2\) done in [C. Bocci et al., J. Algebra 448, 595–617 (2016; Zbl 1387.14151)]. Then they classify all \(\star\)-configurations which may be obtained using Hadamard products.

MSC:

14M99 Special varieties
14T05 Tropical geometry (MSC2010)
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References:

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