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The Hilbert function of some Hadamard products

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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 \(X\star Y\) of two varieties, with \(\dim (X), \dim (Y)\le 1\), 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.

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Authors and Affiliations

  1. Dipartimento di Ingegneria dell’Informazione e Scienze Matematiche, Università di Siena, Via Roma 56, 53100, Siena, Italy

    C. Bocci

  2. Dipartimento di Matematica e Informatica “Ulisse Dini”, Università di Firenze, Viale Morgagni 67/a, 50134, Florence, Italy

    G. Calussi

  3. Dipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli 1, 06123, Perugia, Italy

    G. Calussi, G. Fatabbi & A. Lorenzini

Authors
  1. C. Bocci
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  2. G. Calussi
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  3. G. Fatabbi
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  4. A. Lorenzini
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Corresponding author

Correspondence to C. Bocci.

Additional information

The second author thanks GNSAGA of INdAM and MIUR for their partial support.

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Bocci, C., Calussi, G., Fatabbi, G. et al. The Hilbert function of some Hadamard products. Collect. Math. 69, 205–220 (2018). https://doi.org/10.1007/s13348-017-0200-z

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  • DOI: https://doi.org/10.1007/s13348-017-0200-z

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