JournalspmVol. 76, No. 2pp. 123–141

On the Hadamard product of degenerate subvarieties

  • Gabriele Calussi

    Università degli Studi di Firenze, Italy and Università di Perugia, Italy
  • Enrico Carlini

    Politecnico di Torino, Italy
  • Giuliana Fatabbi

    Università degli Studi di Perugia, Italy
  • Anna Lorenzini

    Università degli Studi di Perugia, Italy
On the Hadamard product of degenerate subvarieties cover

A subscription is required to access this article.

Abstract

We consider generic degenerate subvarieties XiPnX_i \subset \mathbb P^n. We determine an integer NN, depending on the varieties, and for ngeqNn geq N we compute dimension and degree formulas for the Hadamard product of the varieties XiX_i. Moreover, if the varieties XiX_i are smooth, their Hadamard product is smooth too. For n<Nn < N, if the XiX_i are generically did_i-parameterized, the dimension and degree formulas still hold. However, the Hadamard product can be singular and we give a lower bound for the dimension of the singular locus.

Cite this article

Gabriele Calussi, Enrico Carlini, Giuliana Fatabbi, Anna Lorenzini, On the Hadamard product of degenerate subvarieties. Port. Math. 76 (2019), no. 2, pp. 123–141

DOI 10.4171/PM/2029