The Hilbert function of some Hadamard products

• Autores: Cristiano Bocci, G. Calussi, G. Fatabbi, A. Lorenzini
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 69, Fasc. 2, 2018, págs. 205-220
• Idioma: inglés
• DOI: 10.1007/s13348-017-0200-z
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• Resumen

  • 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.

• Referencias bibliográficas
  • Bocci, C., Calussi, G., Fatabbi, G., Lorenzini, A.: On Hadamard products of linear varieties. J. Algebra Appl. 16(8) (2017). doi:10.1142/S0219498817501559
  • Bocci, C., Carlini, E., Kileel, J.: Hadamard products of linear spaces. J. Algebra 448, 595–617 (2016)
  • Bocci, C., Carrucoli, D.: Gorenstein points via Hadamard products (in preparation)
  • Cueto, M.A., Morton, J., Sturmfels, B.: Geometry of the restricted Boltzmann machine. In: Viana, M., Wynn, H. (eds.) Algebraic Methods in...
  • Cueto, M.A., Tobis, E.A., Yu, J.: An implicitization challenge for binary factor analysis. J. Symb. Comput. 45(12), 1296–1315 (2010)
  • Derksen, H., Sidman, J.: A sharp bound for the Castelnuovo Mumford regularity of subspace arrangements. Adv. Math. 172, 151–157 (2002)
  • Eisenbud, D.: The Geometry of Syzygies. Springer, Berlin (2005)
  • Fatabbi, G., Harbourne, B., Lorenzini, A.: Inductively computable unions of fat linear subspaces. J. Pure Appl. Algebra 219, 5413–5425 (2015)
  • Franceschini, S., Lorenzini, A.: Fat points of \mathbb{P}^n whose support is contained in a linear proper subspace. J. Pure Appl. Algebra...
  • Giuffrida, S., Maggioni, R., Ragusa, A.: On the postulation of 0-dimensional subschemes on a smooth quadric. Pac. J. Math. 155, 251–282 (1992)
  • Horn, R.A., Mathias, R.: Block-matrix generalizations of Schur’s basic theorems on Hadamard products. Linear Algebra Appl. 172, 337–346 (1992)
  • Liu, S.: Inequalities involving Hadamard products of positive semidefinite matrices. J. Math. Anal. Appl. 243, 458–463 (2000b)
  • Liu, S.: On the Hadamard product of square roots of correlation matrices. Econometric Theory 18/19, 4 487 1007/703–704 (2002b/2003)
  • Liu, S., Neudecker, H.: Some statistical properties of Hadamard products of random matrices. Stat. Pap. 42, 475–487 (2001a)
  • Liu, S., Neudecker, H., Polasek, W.: The Hadamard product and some of its applications in statistics. Statistics 26(4), 365–373 (1995a)
  • Liu, S., Trenkler, G.: Hadamard, Khatri-Rao, Kronecker and other matrix products. Int. J. Inf. Syst. Sci. 4(1), 160–177 (2008)
  • Million, E.: The Hadamard product. http://buzzard.ups.edu/courses/2007spring/projects/million-paper.pdf (2007)
  • Perrin, D.: Algebraic Geometry: An Introduction. Springer, Berlin (2007)