Higher order duality and toric embeddings

Alicia Dickenstein[1]; Sandra Di Rocco[2]; Ragni Piene[3]

  • [1] Department of Mathematics, FCEN Universidad de Buenos Aires and IMAS - CONICET Ciudad Universitaria - Pab. I C1428EGA Buenos Aires Argentina
  • [2] Department of Mathematics Royal Institute of Technology (KTH) 10044 Stockholm Sweden
  • [3] CMA/Department of Mathematics University of Oslo P.O.Box 1053 Blindern NO-0316 Oslo Norway

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 1, page 375-400
  • ISSN: 0373-0956

Abstract

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The notion of higher order dual varieties of a projective variety, introduced by Piene in 1983, is a natural generalization of the classical notion of projective duality. In this paper we study higher order dual varieties of projective toric embeddings. We express the degree of the second dual variety of a 2-jet spanned embedding of a smooth toric threefold in geometric and combinatorial terms, and we classify those whose second dual variety has dimension less than expected. We also describe the tropicalization of all higher order dual varieties of an equivariantly embedded (not necessarily normal) toric variety.

How to cite

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Dickenstein, Alicia, Di Rocco, Sandra, and Piene, Ragni. "Higher order duality and toric embeddings." Annales de l’institut Fourier 64.1 (2014): 375-400. <http://eudml.org/doc/275645>.

@article{Dickenstein2014,
abstract = {The notion of higher order dual varieties of a projective variety, introduced by Piene in 1983, is a natural generalization of the classical notion of projective duality. In this paper we study higher order dual varieties of projective toric embeddings. We express the degree of the second dual variety of a 2-jet spanned embedding of a smooth toric threefold in geometric and combinatorial terms, and we classify those whose second dual variety has dimension less than expected. We also describe the tropicalization of all higher order dual varieties of an equivariantly embedded (not necessarily normal) toric variety.},
affiliation = {Department of Mathematics, FCEN Universidad de Buenos Aires and IMAS - CONICET Ciudad Universitaria - Pab. I C1428EGA Buenos Aires Argentina; Department of Mathematics Royal Institute of Technology (KTH) 10044 Stockholm Sweden; CMA/Department of Mathematics University of Oslo P.O.Box 1053 Blindern NO-0316 Oslo Norway},
author = {Dickenstein, Alicia, Di Rocco, Sandra, Piene, Ragni},
journal = {Annales de l’institut Fourier},
keywords = {toric variety; higher order projective duality; tropicalization},
language = {eng},
number = {1},
pages = {375-400},
publisher = {Association des Annales de l’institut Fourier},
title = {Higher order duality and toric embeddings},
url = {http://eudml.org/doc/275645},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Dickenstein, Alicia
AU - Di Rocco, Sandra
AU - Piene, Ragni
TI - Higher order duality and toric embeddings
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 1
SP - 375
EP - 400
AB - The notion of higher order dual varieties of a projective variety, introduced by Piene in 1983, is a natural generalization of the classical notion of projective duality. In this paper we study higher order dual varieties of projective toric embeddings. We express the degree of the second dual variety of a 2-jet spanned embedding of a smooth toric threefold in geometric and combinatorial terms, and we classify those whose second dual variety has dimension less than expected. We also describe the tropicalization of all higher order dual varieties of an equivariantly embedded (not necessarily normal) toric variety.
LA - eng
KW - toric variety; higher order projective duality; tropicalization
UR - http://eudml.org/doc/275645
ER -

References

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