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)

Citations:

Zbl 1408.14191; Zbl 1387.14151
Full Text:

References:

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