In this paper, we address the Hadamard product of linear varieties not necessarily in general position. In P2, we obtain a complete description of the possible outcomes. In particular, in the case of two disjoint finite sets X and X′ of collinear points, we get conditions for X X′ to be either a collinear finite set of points or a grid of |X||X′| points. In P3, under suitable conditions (which we prove to be generic), we show that X X′ consists of |X||X′| points on the two different rulings of a nondegenerate quadric and we compute its Hilbert function in the case |X| = |X′|.

Bocci, C., Calussi, G., Fatabbi, G., Lorenzini, A. (2017). On Hadamard product of linear varieties. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 16(8), 155-175 [10.1142/S0219498817501559].

On Hadamard product of linear varieties

Bocci Cristiano;
2017-01-01

Abstract

In this paper, we address the Hadamard product of linear varieties not necessarily in general position. In P2, we obtain a complete description of the possible outcomes. In particular, in the case of two disjoint finite sets X and X′ of collinear points, we get conditions for X X′ to be either a collinear finite set of points or a grid of |X||X′| points. In P3, under suitable conditions (which we prove to be generic), we show that X X′ consists of |X||X′| points on the two different rulings of a nondegenerate quadric and we compute its Hilbert function in the case |X| = |X′|.
Bocci, C., Calussi, G., Fatabbi, G., Lorenzini, A. (2017). On Hadamard product of linear varieties. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 16(8), 155-175 [10.1142/S0219498817501559].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1072191