In this paper we address the Hadamard product of not necessarily generic linear varieties, looking in particular at its Hilbert function. We find that the Hilbert function of the Hadamard product X⋆Y of two varieties, with dim(X),dim(Y)≤ 1, is the product of the Hilbert functions of the original varieties X and Y . Moreover, the same result is obtained for generic linear varieties X and Y as a consequence of our showing that their Hadamard product is projectively equivalent to a Segre embedding.

Bocci, C., Calussi, G., Giuliana, F., Lorenzini, A. (2018). The Hilbert function of some Hadamard products. COLLECTANEA MATHEMATICA, 69(2), 205-220 [10.1007/s13348-017-0200-z].

The Hilbert function of some Hadamard products

Bocci Cristiano
;
2018-01-01

Abstract

In this paper we address the Hadamard product of not necessarily generic linear varieties, looking in particular at its Hilbert function. We find that the Hilbert function of the Hadamard product X⋆Y of two varieties, with dim(X),dim(Y)≤ 1, is the product of the Hilbert functions of the original varieties X and Y . Moreover, the same result is obtained for generic linear varieties X and Y as a consequence of our showing that their Hadamard product is projectively equivalent to a Segre embedding.
Bocci, C., Calussi, G., Giuliana, F., Lorenzini, A. (2018). The Hilbert function of some Hadamard products. COLLECTANEA MATHEMATICA, 69(2), 205-220 [10.1007/s13348-017-0200-z].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1072193