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.
The Hilbert function of some Hadamard products
CALUSSI, GABRIELE;FATABBI, Giuliana;LORENZINI, Anna
2018
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.File in questo prodotto:
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