Collectanea Mathematica

, Volume 69, Issue 2, pp 205–220 | Cite as

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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Copyright information

© Universitat de Barcelona 2017

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria dell’Informazione e Scienze MatematicheUniversità di SienaSienaItaly
  2. 2.Dipartimento di Matematica e Informatica “Ulisse Dini”Università di FirenzeFlorenceItaly
  3. 3.Dipartimento di Matematica e InformaticaUniversità di PerugiaPerugiaItaly

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