Tropically unirational varieties

J. Draisma; B.J. Frenk

Tropically unirational varieties

J. Draisma, B.J. Frenk

Discrete Algebra and Geometry

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

We introduce tropically unirational varieties, which are subvarieties of tori that admit dominant rational maps whose tropicalisation is surjective. The central (and unresolved) question is whether all unirational varieties are tropically unirational. We present several techniques for proving tropical unirationality, along with various examples.

Original language	English
Title of host publication	Algebraic and Combinatorial Aspects of Tropical Geometry (Proceedings of the Tropical Geometry Workshop, Castro Urdiales, Spain, December 12-16, 2011)
Editors	E. Brugallé, M.A. Cueto, A. Dickenstein, E.M. Feichtner, I. Itenberg
Place of Publication	Providence
Publisher	American Mathematical Society
Pages	109-123
ISBN (Print)	978-0-8218-9146-9
Publication status	Published - 2013
Event	conference; Tropical Geomety Workshop; 2011-12-12; 2011-12-16 - Duration: 12 Dec 2011 → 16 Dec 2011

Publication series

Name	Contemporary Mathematics Series
Volume	589
ISSN (Print)	0271-4132

Conference

Conference	conference; Tropical Geomety Workshop; 2011-12-12; 2011-12-16
Period	12/12/11 → 16/12/11
Other	Tropical Geomety Workshop

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Draisma, J., & Frenk, B. J. (2013). Tropically unirational varieties. In E. Brugallé, M. A. Cueto, A. Dickenstein, E. M. Feichtner, & I. Itenberg (Eds.), Algebraic and Combinatorial Aspects of Tropical Geometry (Proceedings of the Tropical Geometry Workshop, Castro Urdiales, Spain, December 12-16, 2011) (pp. 109-123). (Contemporary Mathematics Series; Vol. 589). American Mathematical Society.

Draisma, J. ; Frenk, B.J. / Tropically unirational varieties. Algebraic and Combinatorial Aspects of Tropical Geometry (Proceedings of the Tropical Geometry Workshop, Castro Urdiales, Spain, December 12-16, 2011). editor / E. Brugallé ; M.A. Cueto ; A. Dickenstein ; E.M. Feichtner ; I. Itenberg. Providence : American Mathematical Society, 2013. pp. 109-123 (Contemporary Mathematics Series).

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abstract = "We introduce tropically unirational varieties, which are subvarieties of tori that admit dominant rational maps whose tropicalisation is surjective. The central (and unresolved) question is whether all unirational varieties are tropically unirational. We present several techniques for proving tropical unirationality, along with various examples.",

author = "J. Draisma and B.J. Frenk",

year = "2013",

language = "English",

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editor = "E. Brugall{\'e} and M.A. Cueto and A. Dickenstein and E.M. Feichtner and I. Itenberg",

booktitle = "Algebraic and Combinatorial Aspects of Tropical Geometry (Proceedings of the Tropical Geometry Workshop, Castro Urdiales, Spain, December 12-16, 2011)",

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Draisma, J & Frenk, BJ 2013, Tropically unirational varieties. in E Brugallé, MA Cueto, A Dickenstein, EM Feichtner & I Itenberg (eds), Algebraic and Combinatorial Aspects of Tropical Geometry (Proceedings of the Tropical Geometry Workshop, Castro Urdiales, Spain, December 12-16, 2011). Contemporary Mathematics Series, vol. 589, American Mathematical Society, Providence, pp. 109-123, conference; Tropical Geomety Workshop; 2011-12-12; 2011-12-16, 12/12/11.

Tropically unirational varieties. / Draisma, J.; Frenk, B.J.

Algebraic and Combinatorial Aspects of Tropical Geometry (Proceedings of the Tropical Geometry Workshop, Castro Urdiales, Spain, December 12-16, 2011). ed. / E. Brugallé; M.A. Cueto; A. Dickenstein; E.M. Feichtner; I. Itenberg. Providence : American Mathematical Society, 2013. p. 109-123 (Contemporary Mathematics Series; Vol. 589).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AB - We introduce tropically unirational varieties, which are subvarieties of tori that admit dominant rational maps whose tropicalisation is surjective. The central (and unresolved) question is whether all unirational varieties are tropically unirational. We present several techniques for proving tropical unirationality, along with various examples.

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Draisma J, Frenk BJ. Tropically unirational varieties. In Brugallé E, Cueto MA, Dickenstein A, Feichtner EM, Itenberg I, editors, Algebraic and Combinatorial Aspects of Tropical Geometry (Proceedings of the Tropical Geometry Workshop, Castro Urdiales, Spain, December 12-16, 2011). Providence: American Mathematical Society. 2013. p. 109-123. (Contemporary Mathematics Series).