Segre-Veronese embeddings of P1 x P1 x P1 and their secant varieties.

Maria Virginia Catalisano; Anthony V. Geramita; Alessandro Gimigliano

Collectanea Mathematica (2007)

  • Volume: 58, Issue: 1, page 1-24
  • ISSN: 0010-0757

Abstract

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In this paper we compute the dimension of all the sth higher secant varieties of the Segre-Veronese embeddings Yd of the product P1 × P1 × P1 in the projective space PN via divisors of multidegree d = (a,b,c) (N = (a+1)(b+1)(c+1) - 1). We find that Yd has no deficient higher secant varieties, unless d = (2,2,2) and s = 7, or d = (2h,1,1) and s = 2h + 1, with defect 1 in both cases.

How to cite

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Catalisano, Maria Virginia, Geramita, Anthony V., and Gimigliano, Alessandro. "Segre-Veronese embeddings of P1 x P1 x P1 and their secant varieties.." Collectanea Mathematica 58.1 (2007): 1-24. <http://eudml.org/doc/41792>.

@article{Catalisano2007,
abstract = {In this paper we compute the dimension of all the sth higher secant varieties of the Segre-Veronese embeddings Yd of the product P1 × P1 × P1 in the projective space PN via divisors of multidegree d = (a,b,c) (N = (a+1)(b+1)(c+1) - 1). We find that Yd has no deficient higher secant varieties, unless d = (2,2,2) and s = 7, or d = (2h,1,1) and s = 2h + 1, with defect 1 in both cases.},
author = {Catalisano, Maria Virginia, Geramita, Anthony V., Gimigliano, Alessandro},
journal = {Collectanea Mathematica},
keywords = {Geometría algebraica; 3-variedades; Inmersiones e inclusiones en variedades; defective threefold; multi-projective space; zero-dimensional schemes; Terracini's lemma},
language = {eng},
number = {1},
pages = {1-24},
title = {Segre-Veronese embeddings of P1 x P1 x P1 and their secant varieties.},
url = {http://eudml.org/doc/41792},
volume = {58},
year = {2007},
}

TY - JOUR
AU - Catalisano, Maria Virginia
AU - Geramita, Anthony V.
AU - Gimigliano, Alessandro
TI - Segre-Veronese embeddings of P1 x P1 x P1 and their secant varieties.
JO - Collectanea Mathematica
PY - 2007
VL - 58
IS - 1
SP - 1
EP - 24
AB - In this paper we compute the dimension of all the sth higher secant varieties of the Segre-Veronese embeddings Yd of the product P1 × P1 × P1 in the projective space PN via divisors of multidegree d = (a,b,c) (N = (a+1)(b+1)(c+1) - 1). We find that Yd has no deficient higher secant varieties, unless d = (2,2,2) and s = 7, or d = (2h,1,1) and s = 2h + 1, with defect 1 in both cases.
LA - eng
KW - Geometría algebraica; 3-variedades; Inmersiones e inclusiones en variedades; defective threefold; multi-projective space; zero-dimensional schemes; Terracini's lemma
UR - http://eudml.org/doc/41792
ER -

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